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

Abstract

The present invention 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, which 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.

Claims

1. 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, wherein 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.

2. The method of claim 1, wherein the sample stage is rotated by an angle that is greater than or equal to: 60°, preferably 90°, more preferably 180°, and most preferably 360°.

3. The method of claim 1, wherein the method comprises the additional step of predetermining the non-vanishing distance with respect to the rotation axis.

4. The method of claim 1, wherein the method comprises the additional step of determining coordinates of the rotation axis on a surface of the photomask.

5. The method of claim 4, wherein determining the coordinates of the rotation axis comprises: a. measuring a first set of coordinates for at least two markings of the photomask by use of a particle beam of a particle beam source, without rotating the photomask; b. rotating the photomask by an angle 0°<θ<180° or 180°<θ<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.

6. The method of claim 5, wherein determining the coordinates of the rotation axis comprises: determining the coordinates of the rotation axis from the first and second sets of measured coordinates of the at least two markings.

7. The method of claim 5, wherein measuring the at least two markings is effected by use of 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.

8. The method of claim 3, wherein predetermining the non-vanishing distance with respect to the rotation axis comprises: determining coordinates of a point of incidence of a particle beam of at least one height sensor on the photomask.

9. The method of claim 8, wherein determining the coordinates of the point of incidence of the particle beam of the at least one height sensor comprises: scanning the sample stage for the purpose of centering the at least one height sensor over at least one of the at least two markings.

10. The method of claim 9, wherein scanning the sample stage comprises a scan path adapted to the at least two markings.

11. The method of claim 1, wherein measuring the height change comprises: displacing the rotation axis under a point of incidence of a particle beam of a particle beam source on the photomask.

12. The method of claim 1, furthermore comprising the following step: interpolating and/or extrapolating the measured height change of the photomask for a value deviating from the predetermined, non-vanishing distance.

13. The method of claim 1, furthermore comprising the following step: measuring a z-coordinate of the photomask on the rotation axis.

14. The method of claim 1, wherein the sample stage is displaceable along at least two axes that are parallel to the chuck surface, and wherein the method furthermore comprises the following steps: a. measuring coordinates of at least two markings of the photomask by use of a particle beam of a 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 from the measured coordinates.

15. The method of claim 5, furthermore comprising 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.

16. The method of claim 14, wherein determining the affine transformation comprises: 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.

17. The method of claim 1, wherein the sample stage is displaceable along at least two axes that are parallel to a chuck surface of the sample stage, and wherein the method furthermore comprises 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.

18. The method of claim 17, furthermore comprising 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.

19. 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, the device comprising: 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.

20. A computer program comprising instructions which, when they are executed by a computer system, cause the computer system to carry out the method steps of claim 1.

Description

DESCRIPTION OF DRAWINGS

[0067] The detailed description that follows describes currently preferred exemplary embodiments of the invention with reference to the drawings, wherein:

[0068] FIG. 1 illustrates a schematic view of an exemplary sample stage having three translation axes and one rotation axis;

[0069] FIG. 2 presents a schematic section through the exemplary sample stage from FIG. 1;

[0070] FIG. 3 represents the various coordinates of the coordinate systems within an exemplary sample stage and the coordinate system associated with a photomask;

[0071] 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;

[0072] FIG. 5 schematically illustrates the measurement of the z-coordinate by use of the height sensor for various mask patterns;

[0073] FIG. 6 illustrates a plan view of one type of a marking with the associated reference point thereof;

[0074] FIG. 7 shows a plan view of an exemplary photomask having three markings;

[0075] FIG. 8 illustrates a first example of the scanning of a height sensor within the marking from FIG. 6;

[0076] FIG. 9A illustrates the first part of the flow diagram of the scanning of the height sensor in accordance with the first example from FIG. 8;

[0077] FIG. 9B reproduces the second part of the flow diagram of the scanning of the height sensor in accordance with the first example from FIG. 8;

[0078] FIG. 10 elucidates a second example of the scanning of a height sensor within the marking from FIG. 6;

[0079] FIG. 11 shows a plan view of the photomask from FIG. 7 in a state rotated by 90°;

[0080] FIG. 12 presents a plan view of the photomask from FIG. 7 after a rotation with an arbitrary rotation angle;

[0081] FIG. 13 schematically elucidates a translation induced by a rotation;

[0082] 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;

[0083] 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;

[0084] 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;

[0085] FIG. 17 represents a flow diagram of the method according to the invention for determining an alignment of a photomask on a sample stage;

[0086] FIG. 18A shows the first part of the flow diagram from FIG. 17 with details being specified to a greater degree; and

[0087] FIG. 18B illustrates the second part of the flow diagram from FIG. 17 with details being specified to a greater degree.

DETAILED DESCRIPTION

[0088] 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.

[0089] 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.

[0090] 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.

[0091] 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.sub.b, y.sub.b, z.sub.b relates to the baseplate 205 of the sample stage 100 from FIG. 1.

[0092] 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.

[0093] 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.sub.w, y.sub.w, z.sub.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.sub.ch, y.sub.ch, z.sub.ch.

[0094] 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.

[0095] 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.

[0096] The arrow u directed towards the right describes the u-coordinate of the mask coordinate system in FIG. 2. The coordinates x.sub.ch and y.sub.ch 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.sub.b, y.sub.b, z.sub.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.

[0097] 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.sub.b, y.sub.b, z.sub.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.sub.w, y.sub.w, z.sub.w, wherein the index w stands for “wedge.” Relative to the coordinate system of the baseplate 110, 205, the coordinate system x.sub.w, y.sub.w, z.sub.w can have translations in all three spatial directions.

[0098] 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.sub.ch, y.sub.ch, z.sub.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.

[0099] 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.

[0100] 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.sub.ch, y.sub.ch, z.sub.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.

[0101] 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.

[0102] 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).

[0103] 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.

[0104] 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.

[0105] 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.

[0106] 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>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.

[0107] Furthermore, the device 400 comprises the exemplary sample stage 100, which is not represented in FIG. 4. Furthermore, the coordinate system x.sub.b, y.sub.b, z.sub.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.sub.w represents the height change of the photomask 410 on account of the oblique or skewed position thereof.

[0108] 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.

[0109] 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.

[0110] 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.

[0111] 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.

[0112] 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.

[0113] 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.

[0114] 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.

[0115] 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.

[0116] 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.sub.1, v.sub.1, u.sub.2, v.sub.2 and u.sub.3, v.sub.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.

[0117] 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.

[0118] 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.sub.1, y.sub.1 and x.sub.2, y.sub.2. With the aid of the two measured reference points x.sub.1, y.sub.1 and x.sub.2, y.sub.2 and also the reference points u.sub.1, v.sub.1 and u.sub.2, v.sub.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.sub.1, y.sub.1 and x.sub.2, y.sub.2 with the reference points u.sub.1, v.sub.1 and u.sub.2, v.sub.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.

[0119] The established description of affine coordinates is given in a matrix representation using homogeneous coordinates:

[00001]$\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}{a}_0& a_1& a_2\\ b_0& b_1& b_2\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]$

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:

[00002]$\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}s.Math.\cos \alpha & -s.Math.\sin \alpha & a\\ s.Math.\sin \alpha & s.Math.\cos \alpha & b\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]$

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.

[0120] 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.

[0121] The coordinates of an identified defect u.sub.D, v.sub.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.

[0122] 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.

[0123] 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.

[0124] 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.

[0125] 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. 9A and 9B 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.

[0126] After the first scan 810, in step 915 the signal detected by the height sensor 460 is analyzed and the distance d.sub.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.sub.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.

[0127] Decision block 935 then involves deciding whether the distance d.sub.1 is greater than d.sub.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.

[0128] 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.

[0129] If, in decision block 935, it is established that the distance d.sub.2 is greater than d.sub.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.

[0130] 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.

[0131] 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.

[0132] 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.

[0133] 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.

[0134] 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.

[0135] 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<θ<180°.

[0136] 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.

[0137] 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.

[0138] 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.

[0139] 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.sub.1i, y.sub.1i and x.sub.2i, y.sub.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.sub.1r, y.sub.1r and x.sub.2r, y.sub.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.sub.i=x.sub.2i−x.sub.1i, Δ.sub.yi=y.sub.2i−y.sub.1i, Δx.sub.r=x.sub.2r−x.sub.1r and Δy.sub.r=y.sub.2r−y.sub.1r. The following relationships additionally hold true: tan(θ.sub.i)=Δy.sub.i/Δx.sub.i, tan(θ.sub.r)=Δy.sub.r/Δx.sub.r and θ=θ.sub.r−θ.sub.i. Accordingly, the rotation angle θ can be determined from the measured reference points 720, 740 of the markings 710, 730.

[0140] The parameters t.sub.x and t.sub.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:

[00003]$\left[\begin{array}{c}{x}_r\\ y_r\\ 1\end{array}\right]=\left[\begin{array}{ccc}s.Math.\cos \theta & -s.Math.\sin \theta & t_x\\ s.Math.\sin \theta & s.Math.\cos \theta & t_y\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_i\\ y_i\\ 1\end{array}\right]$

[0141] 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.sub.x and t.sub.y the following results from the matrix equation above:

t.sub.x=x.sub.r−cos θ.Math.x.sub.i+sin θy.sub.i

t.sub.y=y.sub.r−sin θ.Math.x.sub.i−cos θy.sub.i

The aim then, is to find the coordinates x.sub.c, y.sub.c of the rotation axis for which the following holds true:

x.sub.r=x.sub.i

y.sub.r=y.sub.i

The coordinates of the rotation axis are described by x.sub.c, y.sub.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.sub.c, y.sub.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.

[0142] 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.sub.D, y.sub.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.sub.D, y.sub.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.sub.D, y.sub.D.

[0143] The origin of the coordinate system x.sub.c, y.sub.c, z.sub.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.

[0144] After some conversions and using the conditions specified above for x.sub.i, x.sub.r and y.sub.i, y.sub.r, it is possible to express the coordinates of the central rotation axis x.sub.c, y.sub.c as a function of the translations t.sub.x and t.sub.y and of the rotation angle θ:

[00004]$x_c=-\frac{t_y\left(1+\cos \theta \right)}{2.Math.\sin \theta }+1/2t_x$$y_c=\frac{t_x\sin \theta }{2-2.Math.\cos \theta }+1/2t_y$

In this case, the translation parameters t.sub.x and t.sub.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.

[0145] If, after the parameters t.sub.x, t.sub.y and θ have been determined, the sample stage 100 is displaced such that the rotation axis has the coordinates x.sub.c, y.sub.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.

[0146] FIG. 13 illustrates a translation of a point x.sub.i, y.sub.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.sub.i, y.sub.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.sub.i, y.sub.i and the rotation angle Δθ:

x.sub.it=(x.sub.i−x.sub.c).Math.cos Δθ−(y.sub.i−y.sub.c).Math.sin Δθ+x.sub.c−x.sub.i

y.sub.it=(x.sub.i−x.sub.c).Math.sin Δθ+(y.sub.i−y.sub.c).Math.cos Δθ+y.sub.c−y.sub.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.

[0147] 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.

[0148] 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.

[0149] 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.

[0150] 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.sub.c, y.sub.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.

[0151] 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.sub.max. For θ.sub.max=±90°, it then holds true that γ=90° and the height change as a result of the wobble movement vanishes. For θ.sub.max±180°, the height change of the photomask 700 detected by the height sensor 460 reverses its sign.

[0152] From the lower partial image in FIG. 15, the following can be determined for the maximum height change, the height change Δh.sub.max 1570 detected by the height sensor 460:

Δh.sub.max=d.sub.0.Math.tan(δ+γ−90°)

For the height profile h(θ, d.sub.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.sub.0)=cos(θ−θ.sub.max).Math.d.sub.0.Math.tan(δ+γ−90°)+h.sub.off

or:

h(θ,d.sub.0)=Δh.sub.max.Math.cos(θ−θ.sub.max)+h.sub.off

wherein the parameters θ.sub.max, Δh.sub.max and h.sub.off are initially unknown.

[0153] The diagram 1600 in FIG. 16 shows an example of the measured height profile h(θ, d.sub.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.sub.max, Δh.sub.max and h.sub.off are determined as a result of fitting the measurement data 1610 to the function indicated above.

[0154] 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.sub.0):

[00005]$h\left(\theta ,d\right)=h\left(\theta ,d_0\right).Math.\frac{d}{d_0}$

[0155] 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.

[0156] 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.

[0157] 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.

[0158] 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.

[0159] Both steps 1720 and 1730 are optional steps and are therefore represented with dashed boxes around them in FIG. 17.

[0160] 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.

[0161] The method ends in step 1750.

[0162] Finally, the flow diagram 1800 in FIGS. 18A and 18B reproduces the method explained in FIG. 17 in greater detail. The method begins in step 1805.

[0163] 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.

[0164] 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.

[0165] 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.

[0166] The four steps 1810 to 1825 are optional steps and are therefore illustrated with dashed boxes around them in FIG. 18.

[0167] 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.

[0168] 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.

[0169] In step 1840, the photomask 270, 410, 700 is rotated by an angle 0°<α<180°. The rotation effected is preferably by an angle of 90°.

[0170] 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.

[0171] 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.

[0172] 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.

[0173] In the next step 1860, the sample stage 100 is rotated by a predefined angle and the height change h(θ, d.sub.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.sub.0). The method finally ends at 1870.