DE102019119306A1 - Measuring device for determining positions of markers on a planar measuring object and method for calibrating such a measuring device - Google Patents

Abstract

The invention relates to a measuring device (10) for determining positions of markers (12) on a flat measuring object (14), with (a) a measuring object receptacle (16) and (b) a marker position detection system (20) for detecting a marker position ( P _i ) a marker (12.i) of the measurement object (14), (c) wherein the marker position detection system (20) has an xy measuring unit, which (i) has an x position sensor (24.1) for measuring an x coordinate (x _i ) the marker position (P _i ), (ii) a y position sensor (26.1) for measuring a y coordinate (y _i ) of the marker position (P _i ) and (iii) a marker detection system (22) for detection the marker on the measurement object (14). According to the invention, there is (d) at least one second x-position sensor (24.2) for measuring the x-coordinate (x _i ) of the marker position (P _i ), the second x-position sensor (24.2) from the first x-position sensor in the y-direction (24.1) is spaced apart, and (e) at least one second y-position sensor (26.2) for measuring the y-coordinate (y _i ) of the marker position (P _i ), the second y-position sensor (26.2) in the x-direction from first y-position sensor (26.1) is spaced apart.

Description

The invention relates to a measuring device for determining positions of markers on a flat measuring object, with (a) a measuring object receptacle and (b) a marker position detection system for detecting a marker position of a marker of the measuring object, wherein (c) the marker position detection system has an xy- Measuring unit which has (i) an x-position sensor for measuring an x-coordinate of the marker position, (ii) a y-position sensor for measuring a y-coordinate of the marker position and (iii) a marker detection system for detecting the marker on the measurement object having. According to a second aspect, the invention relates to a method for calibrating such a measuring device.

Measuring devices are used to measure fine structures, for example structures on an exposure mask, which are used to manufacture semiconductor components such as processors. These structures could also be referred to as markers. These measuring devices should have the lowest possible measurement uncertainty. The lower the measurement uncertainty, the more precisely it can be ensured that the actual marker corresponds to a target position, for example on the exposure mask.

Such measuring devices must be calibrated. In order to achieve the lowest possible measurement uncertainty, a so-called self-calibration method is particularly advantageous. A self-calibration method is a method in which the properties of the object used for calibration can be calculated out, so that any position uncertainties of markers on the object used for calibration do not increase the measurement uncertainty of the measuring device.

The disadvantage of many methods for self-calibration is the high expenditure on equipment and / or time.

The invention is based on the object of reducing disadvantages in the prior art.

The invention solves the problem by means of a generic measuring device that has at least one second x-position sensor for measuring an x-coordinate of the marker position, the second x-position sensor being spaced from the first position sensor in the y-direction and the measuring device at least a second y Position sensor for measuring the y-coordinate of the marker position, the second y-position sensor being spaced from the first position sensor in the x-direction.

According to a second aspect, the invention solves the problem by means of a method for calibrating a measuring device according to the invention according to one of the preceding claims and / or for determining a position deviation of markers on a flat measurement object by means of the measurement device, with the steps (a) arranging the flat measurement object a measurement object recording of the measuring device, (b) repeating the steps at least twice, in particular three times: (i) detecting a marker position of a marker by means of a marker position recording device, in particular a microscope, so that first raw position data are obtained, and (ii) moving the flat measurement object and the marker position detection device relative to each other, (c) rotating the flat measurement object about the Z axis relative to the marker position detection system, preferably by 120 ° or 90 °, and performing step (b) on the same markers so that second Raw position data is obtained, and (d) determining Calibration data for correcting systematic measurement deviations of the measuring device and / or of real position data from the raw position data.

The advantage of the invention is that the calibration and / or the determination of the markers on the area measurement object can generally be accelerated.

It is also advantageous that the measurement conditions during calibration do not differ from the measurement conditions during the subsequent measurement. Systematic measurement uncertainties due to a different measurement regime are thus avoided.

In the context of the present description, a measurement object recording is understood to mean a device by means of which the measurement object to be measured can be recorded for measurement.

The marker position detection system is understood to mean, in particular, any system by means of which the marker position of the marker can be determined relative to a predetermined, in particular Cartesian, coordinate system. For example, the marker position detection system comprises a Microscope. The marker detection system can be an optical or other microscope, a tactile sensor, confocal sensor or other sensor for detecting the marker. In other words, it is not necessary for the microscope to take measurements on the basis of electromagnetic radiation. For example, the microscope can also be an atomic force microscope or some other scanning probe microscope.

Calibration data is in particular an x-deviation function that describes a systematic measurement deviation of the first x-position sensor as a function of the y-position, and / or a y-deviation function that describes a systematic measurement deviation of the first y-position sensor as a function of the x- Position describes, understood.

An x-y measuring unit is understood to mean, in particular, a measuring unit by means of which coordinates in a Cartesian coordinate system can be determined. It is possible, but not necessary, for the x-axis to extend perpendicular to the y-axis. In particular, it is also possible for the x-axis and the y-axis to enclose an angle of, for example, 120 ° or 60 ° with one another.

The distance between two adjacent markers must be smaller than the distance between the x position sensors and / or the y position sensors.

According to a preferred embodiment, the measuring device comprises an evaluation unit which is designed to automatically carry out a method with steps (a) repeating steps (a) at least three times. i ) Detecting a marker position of a marker so that (x, y) raw position data are obtained, and (ii) causing the flat measurement object and the marker detection system to move relative to one another, (b) detection of a rotation of the flat measurement object around the Z. Axis relative to the marker position detection system and performing step (a) on the same markers, so that second raw position data are obtained, and (c) calculating an x-deviation function which is a systematic measurement deviation of the first x-position sensor as a function of the describes y-position from the raw position data and / or a y-deviation function, which describes a systematic measurement deviation of the first y-position sensor as a function of the x-position, from the raw position data.

The advantage of this is that the x-deviation function can be used for subsequent measurements in order to calibrate the measuring device.

The evaluation unit is preferably designed to automatically determine real position data in a Cartesian coordinate system from the raw position data. In other words, another possible measurement result is the corrected position of the markers.

It is particularly favorable if (a) the x-position sensors (i) a first x-mirror, which extends in the y-direction and is fastened relative to the measurement object receptacle, and (ii) a second x-mirror, which (preferably extends in the y-direction and) is fastened relative to the marker detection system, comprise, (b) the first x-position sensor is designed to (i) emit a first x-measuring laser beam onto the first x-mirror along the y-axis (ii) emitting a first x reference laser beam onto the second x mirror and (iii) allowing the first x measurement laser beam reflected by the x mirror to interfere with the x reference laser beam reflected by the second x mirror, and that (c) the second x-position sensor is designed to (i) emit a second x-measuring laser beam onto the first x-mirror, (ii) emit a second x-reference laser beam onto the second x-mirror and ( iii) Interfering the second x-measuring laser beam reflected by the x-mirror with the second x reference laser beam.

Preferably, (a) the y-position sensors comprise (i) a first y-mirror, which (preferably extends in the x-direction and) is fastened relative to the measurement object receptacle, (ii) a second y-mirror, which (preferably extends in x -Direction and) is attached relative to the marker position detection system, (b) the first y-position sensor is designed to (i) emit a first y-measuring laser beam onto the first y-mirror, (ii) emit a first y- Reference laser beam on the second y-mirror and (iii) interfering the first y-measurement laser beam reflected by the y-mirror with the first y-reference laser beam, (c) the second y-position sensor is designed for (i ) Emitting a second y-measuring laser beam onto the first y-mirror, (ii) emitting a second y-reference laser beam, in particular onto the second y-mirror, and (iii) for interfering the second y-mirror reflected by the mirror -Measuring laser beam with a second y-reference laser st rahl so that raw position data is obtained.

A particularly high measurement accuracy can be achieved if the x-measurement laser beams are aligned parallel to one another.

It is favorable if the three markers do not lie on a line which, when the measurement object rests on the measurement object receptacle, is parallel to one of the measurement directions of one of the sensors. In other words, for example, no three markers lie parallel to the x-axis in the first support of the measurement object and / or parallel to the y-axis in the second support of the measurement object.

• 1 eine perspektivische schematische Ansicht eines erfindungsgemäßen Messgeräts und die
• 2a und 2b Skizzen zur Erläuterung eines erfindungsgemäßen Verfahrens.

The invention is explained in more detail below with reference to the accompanying drawings. It shows:

• 1 a perspective schematic view of a measuring device according to the invention and
• 2a and 2 B Sketches to explain a method according to the invention.

1 shows a measuring device according to the invention 10 for determining positions P _j (j = 0, 1, ..., N) on a flat measuring object 14th . The measuring device 10 has a target holder 16 , which in the present case has three support points, of which the first support point 18 in 1 is partially visible.

The positions P _j the marker 12 .j are detected using a marker position detection system that is a microscope 22nd having. Using the microscope 22nd it can be recorded whether the respective marker 12 .j is in a defined position to the microscope.

The marker position detection system 20th also comprises a first x-position sensor 24.1, a second x-position sensor 24.2, a first y-position sensor 26.1 and a second y-position sensor 26.2. It is possible, but not necessary, for the measuring device to have further x and / or y position sensors. In the present case, the marker position detection system 20th another x-position sensor 24.3. In the present case, the measuring device has 10 in order to k _x = 3 x position sensors and k _y = 2 y position sensors.

The measurement results of the position sensors 24, 24.2, 24.3, 26.1, 26.2 are sent to an evaluation unit 28 transmitted. This is done, for example, using cables that are not shown.

The measurement object recording 16 is designed as a positioning table so that the measurement object 14th relative to the marker position detection system 20th can be moved.

The measuring device 10 comprises a first x reflector 30.1 and a second x reflector 30.2 as well as a first y reflector 32.1 and a second y reflector 32.2. Will the target 14th by means of the measurement object recording 16 moves, the first x reflector 30.1 and the first y reflector 32.1 also move because they are attached to the measurement object receptacle 16 are attached.

The x position sensors each form an x measurement laser beam 34.i and an x reference laser beam 35.i. The x-measuring laser beams run to the first x-mirror 30.1 and the x-reference laser beams to the second x-mirror 30.2, are reflected there and are brought to interference by the respective x-position sensor 24. In this way, a change in distance in the x direction can be determined with high accuracy.

The y position sensors 26.1, 26.2 each send y measurement laser beams 36.1, 36.2 to the first y mirror 32.1 and y reference laser beam 38.1, 38.2 to the second y mirror 32.2. A change in the distance in the y-direction of the measurement object is also used to allow the laser beams to interfere 14th detected. The microscope 22nd is fixed relative to the position sensors 24 , 26th assembled.

2a shows that the second x mirror 30.1 and the second y mirror 32.1 may deviate from an ideal planar shape. This deviation is due to the mirror typography g (y) or described by f (x). There are the respective coordinates of the positions P _j (j = 0, 1, ..., N). This recording is superimposed with systematic errors. The aim is to describe the systematic errors and / or to determine the corrected positions P _j in a Cartesian coordinate system 15th . The evaluation of the raw position data obtained in this way is described below.

It is assumed that the x-position sensors have a systematic measurement deviation that only depends on the y-positions at which they are at the moment of measurement. In addition, it is assumed that the y position sensors have a systematic measurement deviation that only depends on the x positions.

If a position sensor records a measured value m at a position of a marker, the first index denotes whether the measured value comes from an x position sensor (index x) or a y position sensor (index y). The second index indicates how many position sensors have measured, of which at least two exist for the x-position sensor and the y-position sensor. The third index j is a counting index with which the markers, which could also be called structural elements, are numbered on the measurement object. The fourth index φ indicates the support of the measuring object. The measurement object can be displaced relative to the mirrors 30 and 30.2 or rotated about the Z axis by the angle Φ _φ . The zero angle can be freely selected, for example the angle Φ _{φ of} the measurement object is set as Φ ₁ = 0 ° for the first measurement.

A measurement gives the coordinates of the marker position, which deviates from the position in an ideal coordinate system due to systematic measurement deviations. The coordinates have three indices, the first index S indicates that the coordinate is given in the ideal coordinate system. The second index j is the counting index with which the markers on the target are numbered, the third index φ indicates the support of the measuring object.

The nonlinear, systematic measurement deviations of the y position sensors from the y axis of an ideal, in particular Cartesian, coordinate system as a function of the x position of the measurement is described by a deviation function f (x) . The nonlinear, systematic measurement deviation of the x position sensors from the x axis of the ideal, in particular Cartesian, coordinate system as a function of the y position of the measurement is described by a deviation function g (y) .

beschrieben werden. Es ist ein mögliches Ziel des erfindungsgemäßen Verfahrens, diesen Vektor zu bestimmen.The deviation functions are one result of the method according to the invention f (x) and g (y) . Since the deviation functions can only be determined at discrete points, the deviation functions can be determined by a vector after L · N measurements with k x and y position sensors $$\left(\begin{array}{c}\overrightarrow{G}\left(y\right)\\ \overrightarrow{f}\left(x\right)\end{array}\right)={\left(G\left(y_{111}\right)\mathrm{,\; ...,}G\left(y_{kN\mathrm{L.}}\right),f\left(x_{111}\right)\mathrm{,\; ...}f\left(x_{kN\mathrm{L.}}\right)\right)}^t$$

to be discribed. It is a possible aim of the method according to the invention to determine this vector.

It is possible that the number k _x the x position sensors from the number k _y of the y-position sensors. In this case the calibration vector is after N measurements $$\left(\begin{array}{c}\overrightarrow{G}\left(y\right)\\ \overrightarrow{f}\left(x\right)\end{array}\right)={\left(G\left(y_{111}\right)\mathrm{,\; ...,}G\left(y_{k_{x}N{\mathrm{L.}}_{}}\right),f\left(x_{111}\right)\mathrm{,\; ...}f\left(x_{k_{y}N\mathrm{L.}}\right)\right)}^t$$

In order to record the deviations numerically, the deviation functions are described as the sum of basic functions. The basis functions are preferably linearly independent. They preferably form an orthogonal basis. In the present case, the deviation functions over the lengths of the detected deviations (L _x or L _y ) are described by sine and cosine functions. $$\begin{array}{c}f\left(x\right)={\displaystyle \sum _{l=1}^{\mathrm{M.}-1}\left[c_l\cdot \text{cos}\left(\frac{2\pi lx}{{\mathrm{L.}}_x}\right)+d_l\cdot \text{sin}\left(\frac{2\pi lx}{{\mathrm{L.}}_x}\right)\right]+\frac{d_{\mathrm{M.}}}{2}\cdot \text{cos}\left(\frac{2\pi \mathrm{M.}x}{{\mathrm{L.}}_x}\right)}\\ G\left(y\right)={\displaystyle \sum _{l=1}^{\mathrm{M.}-1}\left[{\alpha }_l\cdot \text{cos}\left(\frac{2\pi ly}{{\mathrm{L.}}_y}\right)+b_l\cdot \text{sin}\left(\frac{2\pi ly}{{\mathrm{L.}}_y}\right)+\frac{b_{{\mathrm{M.}}_y}}{2}\cdot \text{cos}\left(\frac{2\pi \mathrm{M.}y}{{\mathrm{L.}}_y}\right)\right]}\end{array}$$

von dem Parametervektor $\stackrel{\rightharpoonup }{{\lambda }_T}$

ab, in dem die Parameter der Darstellung mittels der Basis-Funktionen gemäß Gleichung (3) stehen $$\overrightarrow{{\lambda }_T}{\left(\overrightarrow{a},\overrightarrow{b},\overrightarrow{c},\overrightarrow{d}\right)}^t={\left(a_1\mathrm{,...,}{a}_M,b_1\mathrm{,...,}{b}_M{}_{-1},c_1\mathrm{...,}{c}_M,d_1\mathrm{,...,}{d}_{M-1}\right)}^t.$$

The calibration vector depends on the equation $$\left(\begin{array}{c}\overrightarrow{G}\left(y\right)\\ \overrightarrow{f}\left(x\right)\end{array}\right)=\underset{\_}{T}\left(x,y\right)\cdot \overrightarrow{{\gamma }_T}{\left(\overrightarrow{a},\overrightarrow{b},\overrightarrow{c},\overrightarrow{d}\right)}^t$$

from the parameter vector $\stackrel{\rightharpoonup }{{\lambda }_T}$

in which the parameters of the representation using the basis functions according to equation (3) are $$\overrightarrow{{\lambda }_T}{\left(\overrightarrow{a},\overrightarrow{b},\overrightarrow{c},\overrightarrow{d}\right)}^t={\left(a_1\mathrm{,\; ...,}{a}_{\mathrm{M.}},b_1\mathrm{,\; ...,}{b}_{\mathrm{M.}}{}_{-1},c_1\mathrm{...,}{c}_{\mathrm{M.}},d_1\mathrm{,\; ...,}{d}_{\mathrm{M.}-1}\right)}^t.$$

It is possible that the number of parameters M _x for describing the deviation function parallel to the Y-axis (f (x)) differs from the number of parameters M _y for describing the deviation function parallel to the X-axis (g (y)) . In this case the parameter vector is: $$\overrightarrow{{\lambda }_T}{\left(\overrightarrow{a},\overrightarrow{b},\overrightarrow{c},\overrightarrow{d}\right)}^t={\left(a_1\mathrm{,\; ...,}{a}_{{\mathrm{M.}}_x},b_1\mathrm{,\; ...,}{b}_{{\mathrm{M.}}_x}{}_{-1},c_1\mathrm{...,}{c}_{{\mathrm{M.}}_y},d_1\mathrm{,\; ...,}{d}_{{\mathrm{M.}}_y-1}\right)}^t$$

If measurements are taken at the jth marker at the angle j = 0 ° with two x and y position sensors and sinγ ≈ γ is assumed to be approximate, the measurement results m obtained can be represented as follows: $$\begin{array}{c}{m}_{x1j1}=G\left(y_{sj1}+d_{x1}\right)+x_{sj1}+{\gamma }_{j1}\cdot d_{x1}+{\gamma }_{\mathrm{M.}}\cdot \left(y_{sj1}+d_{x1}\right)\\ m_{x2j1}=G\left(y_{sj1}+d_{x2}\right)+x_{sj1}+{\gamma }_{j1}\cdot d_{x2}+{\gamma }_{\mathrm{M.}}\cdot \left(y_{sj1}+d_{x2}\right)\\ m_{y1j1}=f\left(x_{sj1}+d_{y1}\right)+y_{sj1}+{\gamma }_{j1}\cdot d_{y1}+{\gamma }_{\mathrm{M.}}\cdot \left(x_{sj1}+d_{y1}\right)\\ m_{y2j1}=f\left(x_{sj1}+d_{y2}\right)+y_{sj1}+{\gamma }_{j1}\cdot d_{y2}+{\gamma }_{\mathrm{M.}}\cdot \left(x_{sj1}+d_{y2}\right)\end{array}$$

The angle γ _j1 describes the relative rotation around the Z-axis of the measurement object _receptacle to the position sensors (or when the marker detection system moves, its relative rotation around the Z-axis to the position sensors) and the associated systematic deviation functions (e.g. mirror topographies) the measurement of the j-th marker compared to the marker detection system (eg microscope) when the measurement object is placed at the angle ₁ = 0 °. The angle γ _M describes the relative deviation of the deviation functions from an orthogonal basis (e.g. the angle between the X mirror and the Y mirror is not 90 °) - therefore it is also referred to as an orthogonality error.

mit $$\overrightarrow{m}={\left(\mathrm{...}{m}_{x1j1}{\text{, m}}_{\text{x2j1}}\mathrm{,...,}{m}_{y1j1},m_{y2j1}\mathrm{,...}\mathrm{....}{m}_{x1j\phi },m_{x2j\phi }\mathrm{,...,}{m}_{y1j\phi },m_{y2j\phi }\mathrm{,...}\right)}^t$$

und $$\begin{array}{c}\underset{\_}{A}=\left(\underset{\_}{T}\underset{\_}{P}\underset{\_}{W}\underset{\_}{S}\right),\\ \overrightarrow{m}=\underset{\_}{T}{\overrightarrow{\lambda }}_T+\underset{\_}{P}{\overrightarrow{\lambda }}_P+\underset{\_}{W}{\overrightarrow{\lambda }}_W+\underset{\_}{S}{\overrightarrow{\lambda }}_{S,}\end{array}$$

wobei die nebeneinander angeordneten Teil-Matrizen T, P, W und S bedeuten, dass sie nebeneinander geschrieben werden. Alle Teil-Matrizen haben (k_x+k_y)*N*L Zeilen. Die Matrix A hat mindestens [(2*M_x-1)+ [(2*M_y-1)]+[2*N]+ [(L-1 )*2] +[L*N]+ +1+Q Spalten, womit ebenso viele Parameter bestimmt werden. Davon werden (2*M_x-1) Parameter zur Beschreibung der Abweichfunktion parallel zur Y-Achse und (2*M_y-1) Parameter zur Beschreibung der Abweichfunktion parallel zur X-Achse, welche durch die Teilmatrix T zur Beschreibung der Abweichfunktionen (im Beispiel Spiegel-Topographien) eingeführt sind. (2*N) Parameter zur Beschreibung der Markerpositionen (X- und Y-Koordinate) im idealen Koordinatensystem, sowie (2*L-2) Parameter zur Beschreibung der Mittelpunktkoordinatenänderungen des Messobjektes bei der φ-ten Orientierung/ Auflage des Messobjektes berücksichtigt und durch die Teilmatrix P eingeführt. (L*N) Parameter zur Beschreibung der relativen Winkelvariationen Messobjektaufnahme zu den Positionssensoren werden berücksichtigt und durch die Teilmatrix W eingeführt. Weitere Parameter zur Beschreibung systematischer Abweichungen, wie 1 Orthogonalitätsfehler und Q weitere systematische Fehler, wobei Q eine natürliche Zahl ist, können berücksichtigt werden und werden durch die Teilmatrix S eingeführt.This equation is in matrix notation $$\overrightarrow{m}=\underset{\_}{\mathrm{A.}}\overrightarrow{\lambda }$$

With $$\overrightarrow{m}={\left(\mathrm{...}{m}_{x1j1}{\text{, m}}_{\text{x2j1}}\mathrm{,\; ...,}{m}_{y1j1},m_{y2j1}\mathrm{,\; ...}\mathrm{....}{m}_{x1j\phi },m_{x2j\phi }\mathrm{,\; ...,}{m}_{y1j\phi },m_{y2j\phi }\mathrm{,\; ...}\right)}^t$$

and $$\begin{array}{c}\underset{\_}{\mathrm{A.}}=\left(\underset{\_}{T}\underset{\_}{P}\underset{\_}{\mathrm{W.}}\underset{\_}{\mathrm{S.}}\right),\\ \overrightarrow{m}=\underset{\_}{T}{\overrightarrow{\lambda }}_T+\underset{\_}{P}{\overrightarrow{\lambda }}_P+\underset{\_}{\mathrm{W.}}{\overrightarrow{\lambda }}_{\mathrm{W.}}+\underset{\_}{\mathrm{S.}}{\overrightarrow{\lambda }}_{\mathrm{S.},}\end{array}$$

where the sub-matrices T, P, W and S arranged next to one another mean that they are written next to one another. All sub-matrices have (k _x + k _y ) * N * L rows. The matrix A has at least [(2 * M _x -1) + [(2 * M _y -1)] + [2 * N] + [(L-1) * 2] + [L * N] + +1 + Q columns, which determine the same number of parameters. Of these, (2 * M _x -1) parameters for describing the deviation function parallel to the Y-axis and (2 * M _y -1) parameters for describing the deviation function parallel to the X-axis, which are defined by the sub-matrix T for describing the deviation functions ( in the example mirror topographies) are introduced. (2 * N) parameters for describing the marker positions (X and Y coordinates) in the ideal coordinate system, as well as (2 * L-2) parameters for describing the center point coordinate changes of the measuring object in the φ-th orientation / support of the measuring object taken into account and performed the sub-matrix P introduced. (L * N) parameters to describe the relative angle variations of the measurement object recording to the position sensors are taken into account and introduced by the sub-matrix W. Further parameters for describing systematic deviations, such as 1 orthogonality error and Q further systematic errors, where Q is a natural number, can be taken into account and are introduced by the sub-matrix S.

The coordinates of the markers in the ideal coordinate system S can be described for a measurement object rotated by the angle Φ _φ with the help of the rotation matrix R _φ and the center point coordinates: $$\left(\begin{array}{c}{x}_{sj\phi }\\ y_{sJ\phi }\end{array}\right)={\underset{\_}{\mathrm{R.}}}_{\phi }\cdot \left(\begin{array}{c}{x}_{sj1}\\ y_{sj1}\end{array}\right)-{\underset{\_}{\mathrm{R.}}}_{\phi }\cdot \left(\begin{array}{c}{t}_{x1}\\ t_{y1}\end{array}\right)+\left(\begin{array}{c}{t}_{x\phi }\\ t_{y\phi }\end{array}\right)$$

im idealen Koordinatensystem muss nicht bekannt sein. Die relative Lageänderung des Messobjektes im idealen Koordinatensystem bei den Messungen φ > 1 wird über die Parameter (r_xφ,r_yφ,...) im Gleichungssystem erfasst: $$\left(\begin{array}{c}{x}_{sj1}\\ y_{sj1}\end{array}\right)={\underset{\_}{R}}_{\phi }^{-1}\cdot \left(\begin{array}{c}{x}_{sj\phi }\\ y_{sj\phi }\end{array}\right)+\left(\begin{array}{c}{r}_{x\phi }\\ r_{y\phi }\end{array}\right)$$

The absolute position of the measurement object, namely $\left(\begin{array}{c}{t}_{x1}\\ t_{y1}\end{array}\right),$

in the ideal coordinate system does not have to be known. The relative change in position of the measuring object in the ideal coordinate system for measurements φ> 1 is recorded using the parameters (r _xφ , r _yφ , ...) in the equation system: $$\left(\begin{array}{c}{x}_{sj1}\\ y_{sj1}\end{array}\right)={\underset{\_}{\mathrm{R.}}}_{\phi }^{-1}\cdot \left(\begin{array}{c}{x}_{sj\phi }\\ y_{sj\phi }\end{array}\right)+\left(\begin{array}{c}{r}_{x\phi }\\ r_{y\phi }\end{array}\right)$$

mit den 2N + (2L-2) Parametern: $${\overrightarrow{\lambda }}_P={\left(x_{S10}\mathrm{,...,}{x}_{SN0},y_{S10}\mathrm{,...,}{y}_{\text{S }N0},r_{x2},r_{y2}\mathrm{,...}{r}_{xL},r_{yL}\right)}^T$$

At least one measurement of all markers recorded in the first measurement must be carried out after the measurement object has been rotated around the Z-axis, preferably by 120 ° or 90 °. Further measurements with a shifted and / or twisted measuring object are possible, but not necessary. In general, a displacement of the measurement object must not be greater than the measurement object itself. It applies $${\left(x_{\mathrm{S.}\mathrm{11,}}\mathrm{...,}{x}_{\mathrm{S.}N\mathrm{L.}},y_{\mathrm{S.}11}\mathrm{,\; ...,}{y}_{\mathrm{S.}N\mathrm{L.}}\right)}^T=\underset{\_}{P}\cdot {\overrightarrow{\lambda }}_P,$$

with the 2N + (2L-2) parameters: $${\overrightarrow{\lambda }}_P={\left(x_{\mathrm{S.}10}\mathrm{,\; ...,}{x}_{\mathrm{S.}N0},y_{\mathrm{S.}10}\mathrm{,\; ...,}{y}_{\text{S.}N0},r_{x2},r_{y2}\mathrm{,\; ...}{r}_{x\mathrm{L.}},r_{y\mathrm{L.}}\right)}^T$$

siehe Gleichung (10). $$\underset{\_}{W}=\left(\begin{array}{ccc}& 0& \\ & ⋮& \\ & d_{xi}& \\ & ⋮& \\ \ddots & 0& \ddots \\ & ⋮& \\ & -d_{yi}& \\ & ⋮& \\ & 0& \end{array}\right)$$

Neben den oben genannten systematischen Abweichungen beschrieben durch die Parameter ${\overrightarrow{\lambda }}_T$

und den Winkelvariationen beschrieben durch die Parameter ${\overrightarrow{\lambda }}_W$

kann mindestens ein weiterer systematischer Fehler rekonstruiert werden. Dieser systematische Fehler kann zum Beispiel die Orthogonalitätsabweichung γ_M der Spiegel sein. In diesem Fall gilt: $$\begin{array}{l}{\overrightarrow{\lambda }}_S={\gamma }_M\hfill \\ \underset{\_}{S}=\left(\begin{array}{c}⋮\\ y_{sj0}+d_{xi}\\ ⋮\\ x_{sj\phi }+d_{yi}\\ ⋮\end{array}\right)\hfill \end{array}.$$

Ein weiterer systematischer Fehler kann eine Winkelabweichung des Messobjektes von dem nicht hinreichend genau erfassten Rotationswinkel des Messobjektes bei der φ-ten Auflage sein, welche durch eine kleine Winkelnäherung α_q beschrieben werden kann. In diesem Fall ist Q=(L-1). Die Messwerte der Positionssensoren lassen sich in diesem Fall durch die Gleichungen (16) beschreiben, was den Gleichungen (7) adaptiert für die φ-ten Auflage des Messobjektes entspricht. $$\begin{array}{c}{m}_{x1j\phi }=g\left(y_{sj\phi }+d_{x1}\right)+\text{cos}\left(\phi \right)\cdot x_{sj1}-sin\left(\phi \right)\cdot y_{sj1}+r_{x\phi }+{\gamma }_{j\phi }\cdot d_{x1}\\ +{\gamma }_M\cdot \left(y_{sj\phi }+d_{x1}\right)+{\alpha }_q\cdot y_{sj\phi }\\ m_{x2j\phi }=g\left(y_{sj\phi }+d_{x2}\right)+\text{cos}\left(\phi \right)\cdot x_{sj1}-\text{sin}\left(\phi \right)\cdot y_{sj1}+r_{x\phi }+{\gamma }_{j\phi }\cdot d_{x2}\\ +{\gamma }_M\cdot \left(y_{sj\phi }+d_{x2}\right)+{\alpha }_q\cdot y_{sj\phi }\\ m_{y1j\phi }=f\left(x_{sj\phi }+d_{y1}\right)+\text{sin}\left(\phi \right)\cdot x_{sj1}+\text{cos}\left(\phi \right)\cdot y_{sj1}+r_{y\phi }-{\gamma }_{j\phi }\cdot d_{y1}\\ +{\gamma }_M\cdot \left(x_{sj\phi }+d_{y1}\right)-{\alpha }_q\cdot x_{sj\phi }\\ m_{y2j\phi }=f\left(x_{sj\phi }+d_{y2}\right)+\text{sin}\left(\phi \right)\cdot x_{sj1}+\text{cos}\left(\phi \right)\cdot y_{sj1}+r_{y\phi }-{\gamma }_{j\phi }\cdot d_{y2}\\ +{\gamma }_M\cdot \left(x_{sj\phi }+d_{y2}\right)-{\alpha }_q\cdot x_{sj\phi }\end{array}$$

At least one sensor per axis is not arranged in line with the marker detection system (microscope). A rotation of the measurement slide and the associated mirror topographies relative to the interferometric sensors around the Z-axis leads to a deviation in the interferometric measurement. The deviation Δm _{xi j φ of} the i-th X-sensor with the φ-th orientation / support of the measuring object when measuring the j-th marker corresponds to the product of the change in angle, assuming a small angle approximation (sin (γ) ≈ γ) γ _jφ and the distance between the measuring line of the sensor and a parallel line which runs through the measuring point of the microscope (so-called Abbe offset). These distances between the sensors (d _xi and d _yi ), see 2a) and 2 B) , are to be determined in a preliminary test. Δm _{xi j φ} = γ _{j φ} · d _xi or Δm _{γi j φ} = -γ _{j φ} · d _γi
This leads to the L * N parameters: ${\overrightarrow{\lambda }}_{\mathrm{W.}}={\left({\gamma }_{11}\mathrm{,\; ...,}{\gamma }_{N1}\mathrm{,\; ...,}{\gamma }_{j\phi }\mathrm{...}\right)}^T,$

see equation (10). $$\underset{\_}{\mathrm{W.}}=\left(\begin{array}{ccc}& 0& \\ & ⋮& \\ & d_{xi}& \\ & ⋮& \\ \ddots & 0& \ddots \\ & ⋮& \\ & -d_{yi}& \\ & ⋮& \\ & 0& \end{array}\right)$$

In addition to the above-mentioned systematic deviations described by the parameters ${\overrightarrow{\lambda }}_T$

and the angle variations described by the parameters ${\overrightarrow{\lambda }}_{\mathrm{W.}}$

at least one further systematic error can be reconstructed. This systematic error can be, for example, the orthogonality deviation γ _{M of} the mirrors. In this case: $$\begin{array}{l}{\overrightarrow{\lambda }}_{\mathrm{S.}}={\gamma }_{\mathrm{M.}}\hfill \\ \underset{\_}{\mathrm{S.}}=\left(\begin{array}{c}⋮\\ y_{sj0}+d_{xi}\\ ⋮\\ x_{sj\phi }+d_{yi}\\ ⋮\end{array}\right)\hfill \end{array}.$$

Another systematic error can be an angular deviation of the measurement object from the not sufficiently precisely recorded rotation angle of the measurement object at the φ-th support, which can be described by a small angle approximation α _q . In this case, Q = (L-1). In this case, the measured values of the position sensors can be described by equations (16), which corresponds to equations (7) adapted for the φth support of the measurement object. $$\begin{array}{c}{m}_{x1j\phi }=G\left(y_{sj\phi }+d_{x1}\right)+\text{cos}\left(\phi \right)\cdot x_{sj1}-sin\left(\phi \right)\cdot y_{sj1}+r_{x\phi }+{\gamma }_{j\phi }\cdot d_{x1}\\ +{\gamma }_{\mathrm{M.}}\cdot \left(y_{sj\phi }+d_{x1}\right)+{\alpha }_q\cdot y_{sj\phi }\\ m_{x2j\phi }=G\left(y_{sj\phi }+d_{x2}\right)+\text{cos}\left(\phi \right)\cdot x_{sj1}-\text{sin}\left(\phi \right)\cdot y_{sj1}+r_{x\phi }+{\gamma }_{j\phi }\cdot d_{x2}\\ +{\gamma }_{\mathrm{M.}}\cdot \left(y_{sj\phi }+d_{x2}\right)+{\alpha }_q\cdot y_{sj\phi }\\ m_{y1j\phi }=f\left(x_{sj\phi }+d_{y1}\right)+\text{sin}\left(\phi \right)\cdot x_{sj1}+\text{cos}\left(\phi \right)\cdot y_{sj1}+r_{y\phi }-{\gamma }_{j\phi }\cdot d_{y1}\\ +{\gamma }_{\mathrm{M.}}\cdot \left(x_{sj\phi }+d_{y1}\right)-{\alpha }_q\cdot x_{sj\phi }\\ m_{y2j\phi }=f\left(x_{sj\phi }+d_{y2}\right)+\text{sin}\left(\phi \right)\cdot x_{sj1}+\text{cos}\left(\phi \right)\cdot y_{sj1}+r_{y\phi }-{\gamma }_{j\phi }\cdot d_{y2}\\ +{\gamma }_{\mathrm{M.}}\cdot \left(x_{sj\phi }+d_{y2}\right)-{\alpha }_q\cdot x_{sj\phi }\end{array}$$

To record these Q = (L-1) parameters, the sub-matrix S is expanded accordingly and results in equation (17) instead of equation (15) (17). $$\begin{array}{c}{\overrightarrow{\lambda }}_s={\left({\gamma }_{\mathrm{M.}},{\alpha }_1,{\alpha }_{\mathrm{L.}-1}\right)}^T\\ \underset{\_}{\mathrm{S.}}=\left(\begin{array}{cc}⋮& \\ \left(y_{sj0}+d_{xi}\right)& ⋮\\ ⋮& 0\\ \left(x_{sj0}+d_{xi}\right)& ⋮\\ ⋮& 0\\ \left(y_{sj\phi }+d_{xi}\right)& ⋮\\ ⋮& y_{sj\phi }\\ \left(x_{sj\phi }+d_{yi}\right)& ⋮\\ ⋮& x_{sj\phi }\end{array}\right)\end{array}$$

Further systematic errors are in the patent US 8 473 237 B2 listed and can be integrated in the same way.

wird aus Gleichung (8) eine Matrix A+ berechnet, für die gilt $$\underset{\_}{A}+\overrightarrow{m}=\underset{\_}{A}+\underset{\_}{A}\overrightarrow{\lambda }=1\overrightarrow{\lambda },$$

wobei 1 eine Einheitsmatrix ist. Der Vektor $\overrightarrow{\lambda }$

enthält insbesondere die gewünschten Parameter der Abweichfunktionen, siehe Gleichung (18).To determine the parameters $$\overrightarrow{\lambda }={\left({\overrightarrow{\lambda }}_T^T,{\overrightarrow{\lambda }}_P^T,{\overrightarrow{\lambda }}_{\mathrm{W.}}^T,{\overrightarrow{\lambda }}_{\mathrm{S.}}^T\right)}^T$$

a matrix A + is calculated from equation (8) for which applies $$\underset{\_}{\mathrm{A.}}+\overrightarrow{m}=\underset{\_}{\mathrm{A.}}+\underset{\_}{\mathrm{A.}}\overrightarrow{\lambda }=1\overrightarrow{\lambda },$$

where 1 is an identity matrix. The vector $\overrightarrow{\lambda }$

contains in particular the desired parameters of the deviation functions, see equation (18).

List of reference symbols

10

Measuring device

12

marker

14th

Measurement object

15th

Cartesian coordinate system

16

Measurement object recording

18th

Support point

20th

Marker position detection system

22nd

microscope

24

x position sensor

26th

y position sensor

28

Evaluation unit

30th

x mirror

32

y mirror

34

x measurement laser beam

35

x reference laser beam

36

y-measurement laser beam

38

y reference laser beam

φ

Running index (1 ... L)

Φ

Rotation angle

g (y)

x-deviation function

f (x)

y-deviation function

i

Running index

j

Running index of the marker (1 ... N)

k _x

Number of x position sensors

k _y

Number of y position sensors

L.

Number of different editions of the measurement object

N

Number of markers

P _j

position

Q

natural number, number of further systematic errors

QUOTES INCLUDED IN THE DESCRIPTION

This list of the documents listed by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent literature cited

• US 8473237 B2 [0049]

Claims (11)

Measuring device (10) for determining positions of markers (12) on a flat measuring object (14), with (a) a measuring object receptacle (16) and (b) a marker position detection system (20) for detecting a marker position (P _i ) of a Markers (12.i) of the measurement object (14), (c) wherein the marker position detection system (20) has an xy measuring unit which (i) an x position sensor (24.1) for measuring an x coordinate (x _i ) the marker position (P _i ), (ii) a y-position sensor (26.1) for measuring a y-coordinate (y _i ) of the marker position (P _i ) and (iii) a marker detection system (22) for detecting the marker on the Measurement object (14), characterized by (d) at least one second x-position sensor (24.2) for measuring the x-coordinate (x _i ) of the marker position (P _i ), the second x-position sensor (24.2) in the y-direction from the first x position sensor (24.1) is spaced, and (e) at least one second y position sensor (26.2) for measuring the y coordinate (y _i ) of the Ma rkerposition (P _i ), wherein the second y-position sensor (26.2) is spaced in the x-direction from the first y-position sensor (26.1). Measuring device (10) Claim 1 , characterized in that the marker position detection system (20) has a microscope (22). Measuring device (10) according to one of the preceding claims, characterized by an evaluation unit (28) which is designed to automatically carry out a method with the steps: (a) repeating the steps at least three times: (i) detecting a marker position (P _i ) a Markers (12), so that raw position data are obtained, and (ii) effecting a movement of the flat measurement object (14) and the marker detection system (22) relative to one another, (b) detection of a rotation of the flat measurement object (14) relative to the Marker position detection system (20) about the z-axis, preferably by 120 ° or 90 °, and performing step (a) on the same markers (12) so that second raw position data are obtained, and (c) calculating an x Deviation function (g (y)), which describes a systematic measurement deviation of at least the first x-position sensor (24.1) as a function of the y-position, from the raw position data and / or a y-deviation function (f (x) ), which is a systemat Describes the measurement deviation of at least the first y-position sensor (24.1) as a function of the x-position, from the raw position data. Measuring device (10) according to one of the preceding claims, characterized in that the evaluation unit (28) is designed to automatically carry out a method with the step: Determining real position data in a Cartesian coordinate system (15) of the measurement object (14) from the raw Position data. Measuring device (10) Claim 1 , characterized in that the position sensors (24.1, 24.2, 26.1, 26.2) are interferometric sensors. Measuring device (10) according to one of the preceding claims, characterized in that (a) the x-position sensors (24.1, 24.2) (i) a first x-mirror (30.1), - which extends in the y-direction and - relative to the Measurement object receptacle (16) is attached, and (ii) a second x-mirror (30.2), - is attached relative to the marker detection system (22), comprise, (b) the first x-position sensor (24.1) is designed for (i ) Emitting a first x-measuring laser beam (34.1) onto the first x-mirror (30.1), (ii) emitting a first x-reference laser beam onto the second x-mirror (30.2) and (iii) interfering with the from the x-mirror (30) reflected first x-measuring laser beam (34.1) with the x-reference laser beam reflected from the second x-mirror (30.2), and that (c) the second x-position sensor (24.2) is designed for (i) emitting a second x-measuring laser beam (34.2) onto the first x-mirror (30.1), (ii) emitting a second x-reference laser beam, in particular onto the second x-mirror (30.2), and (iii) allowing the second x-measuring laser beam (34.2) reflected by the x-mirror (30) to interfere with the second x-reference laser beam, so that raw position data are obtained. Measuring device (10) Claim 6 , characterized in that (a) the y position sensors (26.1, 26.2) (i) comprise a first y mirror (32.1) which - extends in the x direction and - is attached relative to the measurement object receptacle (16), ( ii) comprise a second y-mirror (32.2) which - is fixed relative to the marker detection system (22), (b) the first y-position sensor (26.1) is designed for (i) emitting a first y-measuring laser beam (36.1) onto the first y-mirror (32.1), (ii) emitting a first y-reference laser beam (38.1) onto the second y-mirror (32.2) and (iii) interfering with the y-mirror (32 ) reflected first y-measuring laser beam (36.1) with the first y-reference laser beam (38.1), (c) the second y-position sensor (26.2) is designed for (i) emitting a second y-measuring laser beam (36.2 ) on the first y-mirror (32.1), (ii) emitting a second y-reference laser beam (38.2), in particular on the second y-mirror (32.2), and (iii) for interfering with the vo The mirror reflected the second y-measurement laser beam (36.2) with a second y-reference laser beam (28.2), so that raw position data are obtained. Measuring device (10) Claim 6 or 7th , characterized in that (a) the x-measuring laser beams (34.1, 34.2) are aligned parallel to one another and / or (b) the y-measuring laser beams (36.1, 36.2) are aligned parallel to one another. Method for calibrating a measuring device (10) according to one of the preceding claims and / or for determining a positional deviation of markers (12) on a flat measuring object (14) by means of the measuring device (10), with the steps: (a) arranging the flat measuring object (14) on a measurement object receptacle (16) of the measuring device (10), (b) repeating the steps at least twice, in particular three times: (i) detecting a marker position (P _i ) of a marker (12) by means of a marker position detecting device (20 ), in particular a marker detection system (22), so that first raw position data are obtained, and (ii) moving the flat measurement object (14) and the marker position detection device (20) relative to one another in the X, Y direction, (c) Rotating the planar measurement object (14) relative to the marker detection system (20) about the z-axis and performing step (b) on the same markers (12) so that second raw position data are obtained, and (d) determining calibration data (f (x), g (y), y _M ) for correcting a systematic measurement deviation of the measuring device (10) and / or of real position data from the raw position data. Procedure according to Claim 9 , characterized in that the determination of calibration data comprises the following steps: (a) Determination of an x-deviation function (g (y)) which is a systematic measurement deviation of the at least two x-position sensors (k _x ) as a function of the y Describes position, from the raw position data and / or (b) determining a y-deviation function (f (x)), which describes a systematic measurement deviation of the at least two y-position sensors (k _y ) as a function of the x-position, from the raw position data. Procedure according to Claim 10 , characterized in that the determination of calibration data comprises the following steps: (a) Determination of the relative marker positions (X, Y coordinates in the coordinate system of the measurement object) from the raw position data, (b) Determination of the relative angle variations around the Z-axis between the marker detection system and the measurement object at the various marker positions, (c) determination of the angular deviation between the deviation functions (γ _M ) (and at least one further systematic error).

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