Geometrical instruments – Miscellaneous – Light direction
Reexamination Certificate
1999-04-09
2001-11-20
Gibson, Randy W. (Department: 2859)
Geometrical instruments
Miscellaneous
Light direction
C033S503000, C033S504000, C033S702000, C324S758010, C700S194000, C702S094000, C702S095000, C702S150000
Reexamination Certificate
active
06317991
ABSTRACT:
The invention relates to a method for determining a correction function for rectifying the coordinate-dependent measuring errors of a coordinate-measuring machine by means of selfcalibration.
High-precision coordinate-measuring machines are used in the semiconductor industry for the purpose of measuring the structures on masks or wafers. The precise knowledge of the coordinates of the structures on masks is mandatory in order to be able to carry out controlled fabrication of integrated circuits.
The measured values of these high-precision coordinate-measuring machines have error components which depend on the measuring point, that is to say the measured coordinate itself. In this case, there are systematic error components which result from the design and the selection of the components of the coordinate-measuring machine itself. Thus, for example, known causes of error are deficiencies in the mirror orthogonality and the mirror planes, distortions in the scaling of the measuring axes (so-called cosine errors) and the sagging of the mask used for correction.
High-precision coordinate-measuring machines require coordinate-dependent error correction in order to achieve the highest accuracy in the measurements. Determining this correction is generally achieved by comparison with a standard. However, there is as yet no sufficiently accurate standard in the case of extremely high accuracies such as are required, for example, in the measurement technology of semiconductor substrates. It is known for this purpose to calibrate a coordinate-measuring machine with itself by measuring one and the same object in a plurality of rotary positions. An error correction function generated by selfcalibration is used to detect all the errors of the coordinate-measuring machine, with the exception of a scaling error. The latter can be determined only by comparison with a calibrated length standard.
PRIOR ART
U.S. Pat. No. 4,583,298 describes the selfcalibration of a coordinate-measuring machine with the aid of a so-called calibration plate, on which a grating is arranged. The positions of the grating points are, however, not calibrated. The grating plate is laid onto the object table of the coordinate-measuring machine, and the positions of its grating points are measured. The same grating plate is then rotated further twice or several times by 90° in each case about a rotation axis, and the positions of the grating points are measured in each of the set orientations. The measurement results are rotated back mathematically, and various correction factors and tables are optimized such that the rotated-back data records agree more effectively.
U.S. Pat. No. 4,583,298 closely examines the problem of defective or unreliable corrections. Errors in the measurement of the measured values used to determine the correction are ascertained as the cause. It is shown that a mathematically unique correction can be achieved only when more than two different rotary positions are measured with the aid of the same grating plate, and in the process centers of rotation for the rotations between the rotation axes are sufficiently different. As is known, for this purpose the grating plate is laid onto the object table, and the positions of its grating points are measured in a plurality of orientations of the grating plate. The orientations are, for example, achieved by multiple rotations by 90° about their midpoints. Thereafter, however, the grating plate must be displaced to a completely different position on the object table. There, as already previously known, the measurement of the positions of their grating points is repeated in a plurality of orientations. It is essential in this process that the same grating plate must be displaced on the object table.
This requirement turns out in practice, however, to be disadvantageous; the point is that the simplest thing is to rotate the grating plate by angles at which the external dimensions go over into one another. In this case, the center of rotation is always the midpoint of the grating plate. Thus, for example, in U.S. Pat. No. 4,583,298 a square calibration plate is inserted into a square frame and is set down again in it shifted by 90° after each measurement. All the centers of rotation are thereby identical with the midpoint of the calibration plate. Only when the centers of rotation lie far apart, that is to say their spacings are similar in magnitude to the spacings of the calibration structures, is the error correction better. However, even in the case of realizing clearly differing centers of rotation, the determined correction factors and the result of the correction are never completely satisfactory.
The holding mechanism such as, for example, the square frame must be displaced in order to permit a significant displacement of the centers of rotation. The measuring range also needs to be enlarged by comparison with the undisplaced object in this case. There are substantial disadvantages associated with the measures required for this modification of the coordinate-measuring machine. Thus, there is a problem in fitting a displaceable holding frame for the calibration plate on the object table. Specifically, if other mask holders are present on the sample table (for example vacuum chuck or special multipoint bearing), these would need to be specially dismantled for the calibration measurements. Laying a holding frame onto existing mask holders is likewise not an option, since said holders could be damaged or not offer a flat bearing surface for the holding frame.
The enlargement of the measuring range for the purpose of measuring the calibration plate in the displaced state also presents a problem. It requires costly structural changes which are reflected in the fabrication costs of the machine. The external dimensions of the machine are also enlarged. However, the floor space of the machine directly affects its operating costs, because floor space in the clean room is very costly in the semiconductor industry.
OBJECT
It is therefore the object of the invention to specify a method for determining a correction function for rectifying the coordinate-dependent measuring errors of a coordinate-measuring machine, in which, when carrying out the calibration measurements using the already present, non-displaceable maskholders, rotations of the respective calibration substrate about a single center of rotation suffice without the need also to displace the calibration substrate. An optimum error correction is to be achieved, nevertheless. The aim is to specify a continuous correction function with the aid of which it is possible to correct arbitrary measuring points in the entire measuring range, that is to say also between the points of a calibration grating.
This object is achieved according to the invention by means of the independent Patent claim
1
in the case of a method of the type mentioned at the beginning. Advantageous refinements and developments of the invention are the subject matter of the subclaims.
DESCRIPTION
In mathematical terms, a correction function, depending on the measuring point, for rectifying the coordinate-dependent measuring errors of a coordinate-measuring machine is a two- or three-dimensional function {overscore (K)}({overscore (r)}). The correction function is always continuous and differentiable in practice. Applying this correct ion function {overscore (K)}({overscore (r)}) to a measured defective raw coordinate {overscore (r)} (by which the position vector is meant) of a structure of an arbitrary measurement object produces the associated corrected coordinate {overscore (r)}
corr
={overscore (r)}+{overscore (K)}({overscore (r)}).
In order to determine the correction function {overscore (K)}({overscore (r)}) the latter is approximated by a series expansion of a set of prescribed fit functions {overscore (k)}
i
({overscore (r)}). It therefore holds that:
K
_
(
r
_
)
≈
∑
i
=
0
N
a
i
·
k
_
i
(
r
_
)
,
a
i
=fit parameter and N=number of the prescribed fit funct
Foley & Lardner
Gibson Randy W.
Leica Microsystems Wetzlar GmbH
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