JP6539145B2 - Method of correcting interferometer periodic error and method of acquiring correction parameter - Google Patents

Description

  The present invention relates to a method of correcting an interferometer cycle error and a method of acquiring a correction parameter, and relates to correcting a measurement error of a laser interferometer.

Conventionally, high-precision dimension measurement using a laser interferometer is often used.
Laser interferometers of the Fizeau type, Twyman-green type, etc. are widely used for the inspection of parts for which high shape accuracy is required, such as Si (silicon) wafers for semiconductor manufacturing and high-precision mirrors.
The interferometer 1 for measurement, as shown in FIG. 5, includes a light source 2, a beam splitting element 3, a lens 4, a reference surface 5, a phase shifter 6, and an imaging element 7. The face 8 is arranged. Each of the reference surface 5 and the test surface 8 is a surface orthogonal to the optical axis A of the light source 2.

The light emitted from the light source 2 passes through the beam splitting element 3 and the lens 4 to reach the reference surface 5.
Part of the light reaching the reference surface 5 is reflected by the reference surface 5 to become reference light, passes through the lens 4 and the beam splitting element 3 again, and reaches the imaging element 7.
On the other hand, the other part of the light reaching the reference surface 5 passes through the reference surface 5 and reaches the test surface 8. Then, the light is reflected by the test surface 8 to be measurement light, passes through the reference surface 5, the lens 4 and the beam splitter 3 again, and reaches the image sensor 7.
The reference light and the measurement light from the beam splitting element 3 produce an interference image in the imaging element 7, and this interference image is detected by the imaging element 7.

The interferometer 1 changes the relative phase of the reference light and the measurement light by the phase shifter 6 and analyzes the plurality of interference images acquired at different relative phases to measure the shape of the test surface.
As the phase shifter 6, a mechanical phase shift method of mechanically moving an optical element (the reference surface 5 in FIG. 5) in the direction of the optical axis A, a polarization phase shift method using polarization (see Patent Document 1), etc. There are several methods.

In the phase shifter as described above, some errors exist in the mechanical phase shift method due to the calibration error of the movement amount, and in the polarization phase shift method due to the imperfection of the polarizing element and the like.
It is known that the error (phase shift error) of such a phase shifter becomes a non-linear periodic error which affects the shape measurement by the interferometer.
In FIG. 6, assuming that the horizontal axis is the true value of the shape of the surface to be tested and the vertical axis is the measurement result by the interferometer, the ideal value (broken line) is linear corresponding to the true value, but is measured by the interferometer The actual value (solid line) is the ideal value on which the periodic error is superimposed.

In order to correct such a periodic error, a correction algorithm using a window function has been developed (Non-Patent Document 1).
In the method of Non-Patent Document 1, the effect of periodic error is corrected by applying a window function to the intensity change of the interference image acquired while shifting the phase. The intensity change due to the periodic error has a frequency component different from the intensity change due to the original phase shift. For this reason, it is possible to reduce the influence by application of a window function.

U.S. Pat. No. 7,230,717 Japanese Patent Application Laid-Open No. 2002-013907

Peter de Groot, "Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window", Applied Optics, Optical Society of America, USA, Aug. 1, 1995, Vol. 4730 pages

By the way, the periodic error reduction method by the window function mentioned above generally requires five or more interference images.
The above-mentioned method is widely used in the above-mentioned mechanical phase shift interferometer because it is possible to easily obtain a large number of interference images.
However, in the polarization phase shift type interferometer, it is difficult to obtain five or more interference images, and there is a problem that it is difficult to realize correction of a periodic error using the method.

With respect to such a problem, a calibration method of an interferometer using a dedicated stage that can be applied to a polarization phase shift interferometer has been proposed (see Patent Document 2).
In the method of Patent Document 2, calibration of the step amount of the phase shifter incorporated in the interferometer is performed with high accuracy using a calibration phase shifter using a high precision piezoelectric element drive stage. However, this method requires an expensive calibration phase shifter and a stable measurement environment, and has a problem that it can not be generally used.

  An object of the present invention is to provide a method of correcting an interferometer periodic error and a method of acquiring a correction parameter, which can correct a periodic error without using a large number of interference images or an expensive calibration phase shifter.

  The method of correcting an interferometer periodic error according to the present invention comprises: acquiring a correction parameter for each pixel of the interferometer in order to correct a periodic error in a measurement result of an object to be measured by the interferometer; A method of correcting an interferometer periodic error, comprising: a measurement step of measuring the measurement object by the interferometer; and a correction step of correcting the measurement result obtained in the measurement step with the correction parameter, the correction In the parameter acquiring step, the sample is held in a plurality of postures at different inclination angles with respect to the optical axis of the interferometer, and a plurality of shapes obtained in the preliminary measurement step are preliminary measurement steps for measuring shape data in each orientation. Calculating a difference between the reference shape data and the other shape data for each pixel of the shape data, using any one of the data as the reference shape data; A reference table creating step of creating a reference table by recording, for each of the pixels, the correspondence between a phase change due to inclination and a shape change from the difference for each of the pixels, and the above for each of the pixels recorded in the reference table And a correction parameter recording step of polynomial approximation of the correspondence relationship and recording the coefficient as the correction parameter for each pixel.

In such an embodiment of the present invention, displacement of the optical axis direction can be generated in each pixel of the shape data by the operation of inclining the sample. Then, the correspondence between the phase change due to the inclination and the shape change is recorded and used as a correction parameter, whereby the cyclic error can be corrected.
Therefore, in the present invention, it is not necessary to use a device such as a conventional calibration phase shifter which is displaced with high accuracy along the optical axis, and it is not necessary to have a large number of interference images such as a correction method using a window function. In addition, periodic error correction can be performed.

  In the interferometer periodic error correction method of the present invention, in the correction parameter recording step, Fourier expansion of the correspondence relationship is performed as the polynomial approximation, and a Fourier coefficient in the obtained Fourier series is recorded as the correction parameter for each pixel. In the correction step, the periodic error for each pixel is calculated by the inverse Fourier transform of the Fourier series specified by the correction parameter for each pixel, and the measurement result is corrected with the obtained periodic error. It is preferable to do.

  In the present invention as described above, since the Fourier coefficient is recorded as the correction parameter for each pixel, the calculation of the periodic error in the correction process can be performed easily and accurately, and the recording size of the parameter can be reduced.

  In the interferometer cycle error correction method according to the present invention, in the preliminary measurement step, the sample is held by a holding member, and the holding member is rotated around a rotation axis outside the optical path of the interferometer. Preferably, the sample is held at a plurality of tilt angles.

  In the present invention as described above, if there is a holding member for holding the sample and a mechanism for holding the sample in a rotatable manner, it can be easily implemented. Then, all the pixels can be reliably displaced by setting the rotation axis out of the optical path.

  An interferometer cycle error correction parameter acquisition method according to the present invention is an interferometer cycle error correction parameter acquisition method for acquiring a correction parameter for each pixel for correcting a cycle error in a measurement result of a measurement object by an interferometer. A preliminary measurement step of holding the sample in a plurality of postures at different tilt angles with respect to the optical axis of the interferometer and measuring shape data in each posture; and a plurality of shape data obtained in the preliminary measurement step Among them, any one of them is used as reference shape data, and a difference calculation step of calculating the difference between the reference shape data and other shape data for each pixel of the shape data, and phase change due to inclination from the difference for each pixel A reference table creating step of creating a reference table by recording the correspondence between each of the pixels and the shape change for each pixel, and the correspondence between the pixels recorded in the reference table The polynomial approximation, to the correction parameter recording process of recording the coefficient as the correction parameter for each of the pixels, and performing.

  In the present invention as described above, the effects described in the above-described method for correcting an interferometer periodic error of the present invention can be obtained similarly.

  According to the present invention, it is possible to provide an interferometer cycle error correction method and a correction parameter acquisition method that can correct a cycle error without using a large number of interference images or expensive calibration phase shifters.

FIG. 1 is a schematic view showing an interferometer according to an embodiment of the present invention. The schematic diagram which shows operation | movement of the sample of the said embodiment, and a preparatory measurement process. The flowchart which shows the correction procedure of the periodic error in the said embodiment. The flowchart which shows the correction parameter acquisition process in the said embodiment. The schematic diagram which shows the conventional interferometer and phase shifter. The graph which shows the period error which generate | occur | produces in the conventional interferometer.

Hereinafter, an embodiment of the present invention will be described based on the drawings.
〔Device configuration〕
In FIG. 1, the interferometer 10 includes a light source 12, a beam splitting element 13, a lens 14, a reference surface 15, and an imaging device 17, and a test surface 18 is disposed in the vicinity of the reference surface 15. Each of the reference surface 15 and the test surface 18 is a surface orthogonal to the optical axis A of the light source 12.

In such an interferometer 10, the light emitted from the light source 12 passes through the beam splitting element 13 and the lens 14 to reach the reference surface 15.
Part of the light reaching the reference surface 15 is reflected by the reference surface 15 to become reference light, passes through the lens 14 and the beam splitting element 13 again, and reaches the imaging element 17.

The other part of the light reaching the reference surface 15 passes through the reference surface 15 to reach the test surface 18. Then, the light is reflected by the test surface 18 to be measurement light, passes through the reference surface 15, the lens 14 and the beam splitter 13 again, and reaches the image sensor 17.
The reference light and the measurement light from the beam splitting element 13 produce an interference image in the imaging element 17, and this interference image is detected by the imaging element 17.

When measuring the surface shape of the measurement object using such an interferometer 10, the measurement object is disposed as the test surface 18.
On the other hand, when the periodic error of the interferometer 10 is corrected based on the present invention, the sample 19 is disposed on the test surface 18 in order to obtain the correction parameter.

In order to hold the sample 19, a holding member 20 is installed at an arrangement position of the test surface 18.
The holding member 20 is formed, for example, in an arm shape, and the sample 19 can be attached to and detached from the tip. The holding member 20 is rotatably supported at its end on the side opposite to the side on which the sample 19 is mounted, around the rotation axis 21.

The pivot shaft 21 is disposed in parallel with the test surface 18 outside the area of the test surface 18. In the present embodiment, the pivot shaft 21 extends in the direction perpendicular to the drawing of FIG.
The holding member 20 and the sample 19 can be moved from the state shown by the solid line in FIG. 1 to the state shown by the alternate long and short dash line by rotating around the rotation axis 21.
The pivot shaft 21 may be a specific shaft member or a virtual axis.

An angle detector 22 is provided to detect the angular position (inclination angle θ) of the holding member 20 around the pivot shaft 21.
In order to turn the holding member 20, a driving device 23 may be provided which drives the holding member 20 or the sample 19 held by the holding member 20 in the circumferential direction around the turning shaft 21. In addition, a worker may drive the holding member 20.

  When driving the holding member 20, it is desirable to drive the opposite side of the rotational axis 21 with the sample 19 interposed therebetween. That is, the distance (radius) from the rotation axis 21 which is the rotation center to the position to be driven is larger than the distance from the rotation axis 21 to the sample 19 (surface to be detected 18) and driven on the outer periphery side Is desirable. With such an arrangement, the circumferential displacement on the test surface 18 can be made smaller than the amount of drive displacement in the circumferential direction, and a slight displacement can be generated by the test surface 18.

  In FIG. 2, when the holding member 20 and the sample 19 rotate around the rotation axis 21, the surface to be inspected 18, that is, the surface on the reference surface 15 side of the sample 19 also rotates and approaches the reference surface 15. The arbitrary pixel P of the surface 18 to be detected is displaced by the displacement ΔL in the optical axis A direction by this rotation. The displacement ΔL is a sufficiently small value with respect to the distance L between the reference surface 15 and the test surface 18 indicated by a solid line.

Correction method
Next, a procedure for correcting the periodic error of the interferometer 10 according to the present invention will be described.
In FIG. 3, for correction of the periodic error of the interferometer 10, a correction parameter for each pixel is previously obtained for the interferometer 10 (process S31: correction parameter acquisition step), and after this, the measurement object to be actually measured (Process S32), the shape of the object to be measured is measured by the interferometer 10 (Process S33: Measurement process), and the obtained measurement result is corrected with the previously acquired correction parameter (Process S34: Correction step).

In the present embodiment, the reference position refers to a position where the test surface 18 or the sample 19 is in a solid line in FIG. 1, and a plurality of inclination angles (not shown) The posture of θ (θ = θ1 to θn) is set.
In each inclined posture, the sample 19 and the test surface 18 are rotated by the inclination angle θ with respect to the reference position. That is, in each inclined posture, the angle between the sample 19 and the test surface 18 and the optical axis A is (π / 4−θ).

[Overview of Correction Parameter Acquisition Process]
The correction parameter acquisition process of process S31 of FIG. 3 is performed by each procedure (processes S41 to S40) shown in FIG.
In FIG. 4, first, the sample 19 (see FIG. 1 and FIG. 2) is attached to the holding member 20 and acquired in the reference posture (state of solid line in FIG. 1 and FIG. 2). ). Then, the shape of the test surface 18 of the sample 19 in this reference posture is measured by the interferometer 10 (processing S42).

Next, the sample 19 and the holding member 20 are rotated to change the inclination angle θ (process S43), and the shape of the test surface 18 of the sample 19 in this posture is measured by the interferometer 10 (process S44).
The shape measurement (processes S43 to S44) in such an inclined posture is repeated a plurality of times (three times in the present embodiment) (process S45).

By the above processing S41 to S45, shape measurement of a total of four times including the reference posture is performed, and shape data of four sets (one set of shape data of the reference posture and three sets of shape data in the inclined posture) is obtained Be
The preliminary measurement process of the present invention is configured by these processes S41 to S45.

  In the preliminary measurement step, as shown in FIG. 2, when the sample 19 is in the posture with the inclination angle θ with respect to the reference surface 15, the measurement light reflected by the test surface 18 of the sample 19 is reflected by the reference surface 15. A relative phase difference as shown in the following equation (1) occurs between the reference light and the reference light.

Here, when the test surface 18 of the sample 19 is spread on the xy plane, the rotational axis 21 extends along the y axis, and the distance from the rotational axis 21 to the pixel P is x, the inclined attitude is The result of the shape measurement of the sample 19 in FIG. ₂ is represented by the phase value φ _meas of the following equation (2).

  Here, the three terms on the right side are as follows.

The inclination angle θ can be accurately known by calculating the least square plane of the measured shape data.
In this manner, shape data in one posture can be measured by measuring the phase difference of equation (1) and the shape measurement result of equation (2) for each pixel and recording for all pixels.
Then, by performing measurement of similar shape data in each of the three inclined postures and the reference posture, a plurality of shape data as a preliminary measurement process can be obtained.

  When a plurality of shape data are obtained, the target pixel is sequentially selected in the shape data of the reference posture (processing S46), and calculation of the difference for each pixel with other shape data (processing S47: difference calculation step) and reference table The creation (process S48: reference table creation process) is performed, and the processes S46 to S48 are repeated for all the pixels (process S49).

[Difference calculation step: processing S47]
In the difference calculation step, with respect to the four sets of shape data obtained in the preliminary measurement step (processing S41 to S45), the difference between the reference shape data and the other three sets of shape data for each pixel in the reference shape data ( Calculate 3 sets per pixel.

The inclination angle θ ₁ of the reference shape data and the inclination angle θ ₂ of the other shape data which takes a difference can be expressed by the following equation (6) when the difference with respect to the reference shape data of the shape data is taken.

In the equation (6), the display is omitted because the positions x and y related to the pixel of interest are the same in the equation.
In the equation (6), the second term including φ _tilt on the right side is the phase change given by the change of tilt, and can be calculated from the difference of the least square plane of the measurement result.
Therefore, by removing the inclination component and the component derived from the shape from the measurement result by the above calculation, only the periodic error component can be extracted, and this can be corrected.

[Reference table creation process: process S48]
In the reference table creation step, the correspondence relationship (3 sets for each pixel) between the phase change due to inclination and the shape change is calculated from the difference for each pixel obtained in the difference calculation step (processing S47), and the result is calculated for each pixel Record in and create a reference table.

As the reference table, for example, the phase change due to the inclination is arranged on the horizontal axis, and the shape change of the sample 19 due to the periodic error is arranged on the vertical axis, thereby recording the respective correspondences.
The following equations (7) and (8) are used as phase change and shape change due to inclination. In each equation, the angle θ ₁ is the inclination angle of the reference attitude, and the angle θ is the inclination angle of the inclination attitude obtained by the difference. In the equation (8), the angle θ is converted to the phase value φ by the equation (1) .

[Correction parameter recording step: processing S40]
In the correction parameter recording step, the correspondence relationship for each pixel recorded in the reference table is polynomial-approximated, and the coefficient is recorded as a correction parameter for each pixel.
In this embodiment, Fourier series expansion up to an arbitrary approximation order n _max is used as a polynomial approximation.

The equation (8) recorded in the reference table is approximated by the following equation (9) by the Fourier series expansion up to the approximation order n _max .

When equation (9) is obtained, the Fourier coefficients cn and dn are recorded for each pixel as a correction parameter for each pixel.
Thus, the correction parameter for each pixel can be acquired.

[Error correction of measurement object: processing S32 to S34]
Returning to FIG. 3, when acquisition of the correction parameter for each pixel for the interferometer 10 (process S31: correction parameter acquisition step) is performed, actual correction processing on the measurement object can be performed.

  The correction of the periodic error of the interferometer 10 is, as described above, placing the measuring object to be actually measured (processing S32), and measuring the shape of the measuring object by the interferometer 10 (processing S33: measuring step) The process of correcting the obtained measurement result with the previously acquired correction parameter is performed (process S34: correction process).

That is, the shape measurement of the measurement object in the processes S32 to S33 is performed.
The phase value φ _meas obtained as a result of this shape measurement is expressed by the following equation (10) as the sum of the phase value φ of the sample shape, the phase change φ _tilt due to inclination, and the periodic error δ φ.

Among these values, the value to be finally obtained as the surface shape of the sample 19 (the shape of the test surface 18) is a phase value φ derived from the sample 19. Among other components, the phase change φ _tilt due to the _tilt can be known from the least square plane. The periodic error δφ can be calculated by performing the inverse Fourier transform of the Fourier series obtained by Equation (9).
Therefore, after the shape measurement of the object to be measured (processing S32 to S33), in the correction step (processing S34), the phase value φ is obtained from the phase value φ _{meas of the} result using equation (10). It is possible to obtain a true value not including the periodic error δφ of the surface of the object (the test surface 18).

According to such an embodiment, it is possible to cause displacement of each pixel of shape data in the optical axis direction by the operation of inclining the sample 19. Then, the correspondence between the phase change φ _tilt due to the _tilt and the shape change Δ に よ る is recorded and used as a correction parameter, whereby the periodic error δφ can be corrected.
Therefore, in the present embodiment, it is not necessary to use a device such as a conventional calibration phase shifter displaced with high accuracy along the optical axis A, and a large number of interference images such as a correction method using a window function are required. It is possible to correct the periodic error δφ without taking it.

Further, in the present embodiment, since the Fourier coefficients cn and dn are recorded as the correction parameters for each pixel, the calculation of the periodic error in the correction process can be performed easily and accurately, and the recording size of the parameters can be reduced.
Furthermore, in the present embodiment, if there is the holding member 20 for holding the sample 19 and the mechanism for holding the sample rotatably, this can be easily implemented.
Then, all the pixels can be reliably displaced by setting the rotation axis 21 out of the light path.

The present invention is not limited to the above-described embodiment, and modifications and the like within the scope in which the object of the present invention can be achieved are included in the present invention.
For example, in the embodiment, three rotation operations are performed in the preliminary measurement step, one set of shape data of the reference posture is measured, and three sets of shape data in the inclined posture are measured. The number of sets of shape data may be changed as appropriate.

  In the above embodiment, the reference shape data is measured in the reference posture (orthogonal to the optical axis A) shown by the solid line in FIG. 1, and the difference with the other shape data in the inclined posture is taken. Shape data may be measured in a plurality of inclined postures with different angles, and any one of them may be selected as reference shape data later, and the difference with other shape data may be taken.

  Furthermore, the polynomial approximation in the correction parameter recording step is not limited to the triangular polynomial approximation such as the Fourier series expansion, and other approximation methods such as the least square method may be used.

  The present invention relates to a method of correcting an interferometer cycle error and a method of acquiring a correction parameter, which can be used to correct a measurement error of a laser interferometer.

DESCRIPTION OF SYMBOLS 1 ... Interferometer, 10 ... Interferometer, 12 ... Light source, 13 ... Beam division element, 14 ... Lens, 15 ... Reference surface, 17 ... Image sensor, 18 ... Test surface, 19 ... Sample, 2 ... Light source, 20 ... Holding member, 21: rotation axis, 22: angle detector, 23: drive device, 3: beam splitting element, 4: lens, 5: reference surface, 6: phase shifter, 7: imaging device, 8: test surface , A: optical axis, cn, dn: Fourier coefficient, L: distance, _nmax : approximate order, P: pixel, ΔL: displacement due to inclination, ΔΦ: shape change, δφ: periodic error, θ: inclination angle, θ1: Tilt angle, θ 2 ... tilt angle, φ ... phase value indicating surface shape, φ _meas ... measured phase value, φ _tilt ... phase change due to _tilt .

Claims (4)

In order to correct a periodic error in the measurement result of the measurement object by the interferometer, a correction parameter acquisition step of acquiring a correction parameter for each pixel of the interferometer, and a measurement of measuring the measurement object by the interferometer A method for correcting an interferometer periodic error, comprising: a process; and a correction process for correcting the measurement result obtained in the measurement process with the correction parameter,
In the correction parameter acquisition step,
A preliminary measurement step of holding the sample in a plurality of postures at different tilt angles with respect to the optical axis of the interferometer and measuring shape data in each posture;
A difference calculation step of using any one of a plurality of shape data obtained in the preliminary measurement step as reference shape data, and calculating a difference between the reference shape data and other shape data for each pixel of the shape data; ,
A reference table creation step of creating a reference table by recording, for each pixel, the correspondence between a phase change due to inclination and a shape change from the difference for each pixel;
Performing a correction parameter recording step of polynomial-approximating the correspondence relationship of the pixels recorded in the reference table and recording the coefficient as the correction parameter of the pixels; Correction method. In the interferometer periodic error correction method according to claim 1,
In the correction parameter recording step, Fourier expansion of the correspondence relationship is performed as the polynomial approximation, and Fourier coefficients in the obtained Fourier series are recorded as the correction parameter for each pixel.
In the correction step, a periodic error for each pixel is calculated by inverse Fourier transform of the Fourier series specified by the correction parameter for each pixel, and the measurement result is corrected with the obtained periodic error. Interferometer periodic error correction method. In the interferometer periodic error correction method according to claim 1 or 2,
In the preliminary measurement step, the sample is held by a holding member, and the sample is held at a plurality of inclination angles by rotating the holding member around a rotation axis outside the optical path of the interferometer. A method of correcting an interferometer cycle error as a feature. What is claimed is: 1. A method of acquiring a correction parameter of an interferometer periodic error, which acquires a correction parameter for each pixel, for correcting a periodic error in a measurement result of a measurement object by an interferometer.
A preliminary measurement step of holding the sample in a plurality of postures at different tilt angles with respect to the optical axis of the interferometer and measuring shape data in each posture;
A difference calculation step of using any one of a plurality of shape data obtained in the preliminary measurement step as reference shape data, and calculating a difference between the reference shape data and other shape data for each pixel of the shape data; ,
A reference table creation step of creating a reference table by recording, for each pixel, the correspondence between a phase change due to inclination and a shape change from the difference for each pixel;
Performing a correction parameter recording step of polynomial-approximating the correspondence relationship of the pixels recorded in the reference table and recording the coefficient as the correction parameter of the pixels; Correction parameter acquisition method.

Images