CN110764372B - Calibration method of immersion lithography machine polarization aberration detection system - Google Patents
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Abstract
The invention provides a calibration method of a polarization aberration detection system of an immersion lithography machine, and belongs to the field of optical detection. The PSG in the detection system is composed of a polaroid and a wide-angle quarter-wave plate, and the design is suitable for large-angle incidence. In the intrinsic value calibration process, the calibration sample adopts the wide-angle quarter-wave plate to meet the operating condition of the intrinsic value calibration method when the incidence angle is large, and the calibration of the high-numerical-aperture polarization imaging system can be realized. In addition, in the calibration method, the calibration strategy is implemented by using a traditional quarter-wave plate and a wide-angle quarter-wave plate in combination with the calibration samples in each step; the calibration method has the advantages that the calibration of the polarization state generator and the polarization state analyzer is realized, the calibration of the collimating mirror is also completed, the strategy is suitable for the calibration of the polarization aberration of any high-numerical-value hollow aperture imaging system, the application range is expanded, the operation is simple, the feasibility is strong, and the calibration precision is high.
Description
Technical Field
The invention belongs to the technical field of optical detection, and particularly relates to a calibration method of a polarization aberration detection system of an immersion lithography machine.
Background
The core equipment for manufacturing large scale integrated circuits is the lithography machine, the core component of which is the projection lithography objective. The promotion of the integrated circuit node prompts the Numerical Aperture (NA) of the photoetching objective to be continuously increased, when the NA is increased to a certain degree, the influence of the polarization state of the imaging light beam on the imaging quality becomes non-negligible, the polarization aberration of the projection objective needs to be accurately measured, and then the projection objective is reasonably controlled, and the imaging performance of the projection objective is improved.
Related patents (chinese patent CN103197512A) and (CN104281011A) disclose methods for obtaining polarization aberration of lithography projection system, but these methods can only detect partial information of polarization aberration of projection system, and cannot be used for measurement of polarization aberration of actual lithography projection objective. The literature (Nomura, h., and Higashikawa, i., "Mueller matrix polarization for imaging polarization systems at the wafer plane," proc.spie 7520,752012, (2009)) proposes the online measurement of projection objective polarization aberrations with a Mueller matrix polarizer, which consists of a polarization mask, a collimator, a quarter-wave plate, a polarization beam splitter prism and a CCD, wherein the polarization mask as polarization state generator PSG consists of a four-piece polarizer and a four-piece wide-angle quarter-wave plate together, and the polarizer is preceded and followed; the collimator couples the pupil of the projection objective to the CCD photosensitive surface and collimates the high NA imaging light beam into a parallel light beam; the quarter-wave plate and the polarization beam splitter prism form a polarization state analyzer PSA, which analyzes the Stokes parameters of the parallel beams behind the collimator lens by a Fourier analysis method. In the measurement process, the PSG generates 16 incident beams with known polarization states in total, the Stokes parameters of each incident beam after the incident beam exits from the collimator are measured by the PSA and the CCD camera, and the Mueller matrix of the projection objective can be obtained by performing mathematical operation on the incident and exiting Stokes parameters.
However, the calibration of the instrument is not considered in the measurement method, and the measured mueller matrix includes the influence of the collimating mirror, so that at present, no mature and feasible method is available for calibrating the collimating mirror.
Disclosure of Invention
In order to solve the technical problem, the invention provides a calibration method of a polarization aberration detection system of an immersion lithography machine, which not only realizes the calibration of a polarization state generator and a polarization state analyzer, but also completes the calibration of a collimating mirror, and in the calibration method, a traditional quarter-wave plate and a wide-angle quarter-wave plate are jointly used for calibrating a calibration sample in each step.
The technical scheme for realizing the invention is as follows:
a polarization aberration detection system of an immersion lithography machine mainly comprises an illumination device, a polarization state generator PSG, a projection objective, a collimating lens coupled with the projection objective, a polarization state analyzer PSA and a CCD detector; the PSG consists of a polarizer and a wide-angle quarter-wave plate, because the numerical aperture of the object side of the projection objective is large, the incident angle of the illumination beam at the mask is not normal incidence, and the phase delay error can be generated by the traditional quarter-wave plate; the polarization state analyzer PSA is composed of a conventional quarter-wave plate and a polarizing prism.
The instrument matrixes of the PSG and the PSA are respectively G and A, and the Mueller matrix of the collimating lens for coupling the projection objective and the projection objective is respectively MpAnd Mc。
The calibration method of the polarization aberration detection system of the immersion lithography machine is characterized by comprising the following steps:
the method comprises the following steps: the composite calibration method is used for calibrating the polarization aberration detection system of the immersion lithography machine by combining a Fourier analysis method and an eigenvalue calibration method;
1.1, a Fourier analysis method is used for calibrating a polarization state generator PSG and a polarization state analyzer PSA, obtaining instrument matrixes G and A, and obtaining a fast axis azimuth angle error epsilon of wave plates in the polarization state generator PSG and the polarization state analyzer PSA through obtaining1And ε2Error of retardation epsilon4And ε5And the transmission axis azimuth angle error epsilon of the polarizing prism in the polarization state analyzer PSA3(ii) a The instrument matrices G and a used to solve the polarization state generator PSG and the polarization state analyzer PSA;
the method comprises the following specific steps:
1.1.1, rotating the wave plate in the polarization state generator PSG and the polarization state analyzer PSA to the air, wherein the ratio of the rotation angle of the wide-angle quarter-wave plate in the polarization state generator PSG to the rotation angle of the quarter-wave plate in the polarization state analyzer PSA is 1: 5;
let us say that the retardation of the wide-angle quarter-wave plate in the polarization state generator PSG is delta1Retardation of the quarter-wave plate in the polarization analyzer PSA is delta2The following formula:
from equation (2), the errors of the devices in the PSG and PSA, i.e., the fast axis azimuth angle errors ε of the wave plates in the PSG and PSA, can be obtained1And ε2Error of retardation epsilon4And ε5And the transmission axis azimuth angle error epsilon of the polarizing prism in the polarization state analyzer PSA3。
Secondly, the calculated errors are brought into the instrument matrixes G and A of the polarization state generator PSG and the polarization state analyzer PSA, so that the calibration of the polarization state generator PSG and the polarization state analyzer PSA is completed, and the instrument matrixes G and A of the polarization state generator PSG and the polarization state analyzer PSA are obtained.
Step two, solving instrument matrixes G and A of the polarization state generator PSG and the polarization state analyzer PSA by a method different from the method in the step one, namely calibrating the polarization aberration detection system of the immersion lithography machine by using a multi-step eigenvalue calibration method to obtain the instrument matrixes G and A;
and respectively placing the calibration sample S between the polarization state generator PSG and the projection objective lens and between the collimating lens and the polarization state analyzer PSA, respectively carrying out an eigenvalue calibration method, and then solving the instrument matrixes G and A according to matrix operation.
The method comprises the following specific steps:
2.1: placing a calibration sample S between a polarization state generator PSG and a projection objective, wherein the polarization state generator PSG is used as a group, and the instrument matrix is M21; the projection objective, the collimator, and the polarization analyzer PSA are a set, and the instrument matrix is M22, where M21 and M22 can be expressed as:
M21＝G, (7)
M22＝A·Mc·Mp. (8)
one eigenvalue calibration was performed to obtain M21 and M22.
2.2: placing a calibration sample S between a collimating mirror and a polarization state analyzer PSA, wherein a polarization state generator PSG, a projection objective and the collimating mirror are used as a group, and the instrument matrix is M23; the polarization state analyzer PSA is used as a group, and its instrument matrix is M24, where M23 and M24 are expressed as:
M23＝Mc·Mp·G, (9)
M24＝A. (10)
again, eigenvalue calibration is performed, and the instrument matrices G and a of the polarization state generator PSG and polarization state analyzer are obtained from equations (7) and (10) by matrices M21 and M24.
Bringing the results of step one or step two into stepStep three, completing the calibration of the collimating mirror, namely obtaining the Mueller matrix M of the collimating mirrorcFinally, the polarization phase difference M of the projection objective is accurately obtainedp。
The third step comprises the following specific steps:
3.1 Place the calibration sample S between the projection objective and the collimator lens to perform eigenvalue calibration, in this process, set the polarization state generator PSG and the projection objective as one set, and set its instrument matrix as M11, and set the collimator lens and the polarization state analyzer PSA as the other set, and set its instrument matrix as M12. Then M11 and M12 can be expressed as:
M11＝Mp·G, (3)
M12＝A·Mc. (4)
and (5) obtaining M11 and M12 by an eigenvalue calibration method.
3.2 combining the PSG obtained in the first step or the second step with the instrument matrixes G and A of the PSA, and obtaining M through matrix operationpAnd McAs shown in the following formula:
Mp＝M11·G-1, (5)
Mc＝A-1·M12. (6)
the calibration of the polarization aberration detection system of the immersion lithography machine is completed, namely instrument matrixes G and A of a polarization state generator PSG and a polarization state analyzer PSA and a Mueller matrix M of a collimating mirror are obtainedcFinally, the polarization phase difference M of the projection objective is accurately obtainedp。
In general, the calibration sample S is selected from the optimal reference samples given in the prior publications: air, a polaroid with the transmission axis direction being the horizontal direction, a polaroid with the transmission axis direction being the vertical direction and a quarter wave plate with the fast axis azimuth angle being 30 degrees; but of note in the present invention are: the calibration samples in the third step are air, a polaroid and a wide-angle quarter-wave plate; and the calibration samples in step two, namely the air, the polaroid and the wide-angle quarter-wave plate in step 2.1, and the calibration samples in step 2.2, namely the air, the polaroid and the conventional quarter-wave plate.
Has the advantages that:
1. the invention provides a calibration method of a polarization aberration detection system of an immersion lithography machine, which not only realizes the calibration of a polarization state generator and a polarization state analyzer, but also completes the calibration of a collimating lens, and finally can accurately acquire all information of the polarization aberration of a projection objective.
2. In the eigenvalue calibration of the polarization aberration detection system of the immersion lithography machine, the wave plate in the calibration sample adopts the wide-angle quarter wave plate, is suitable for large-angle incidence, meets the operating condition of the eigenvalue calibration method during the large-angle incidence, and can realize the calibration of the high-numerical-aperture polarization imaging system. In the calibration method, the traditional quarter-wave plate and the wide-angle quarter-wave plate are used in combination in each step for calibration, and the strategy is suitable for the calibration of the polarization aberration of any high-numerical-value hollow aperture imaging system, so that the application range is expanded, and the operability is enhanced.
Drawings
FIG. 1 is a schematic diagram of a projection objective polarization aberration detection system of an immersion lithography machine;
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
The immersion lithography machine polarization aberration detecting system is characterized in that:
the polarization aberration detection system of the immersion lithography machine in fig. 1 mainly includes an illumination device 101, a polarization state generator PSG102, a projection objective 103, a collimator 104 coupled with the projection objective, a polarization state analyzer PSA105 and a CCD detector 106; the polarization state generator PSG102 is composed of a polarizer 221 and a wide-angle quarter-wave plate 222, because the projection objective 103 has a large numerical aperture at the object side, the incident angle of the illumination beam at the mask is not normal incidence, and the conventional quarter-wave plate can generate a phase retardation error; the polarization state analyzer PSA105 is composed of a conventional quarter wave plate 321 and a polarizing prism 322.
Let G and A be the instrument matrices of the polarization state generator PSG102 and the polarization state analyzer PSA105, respectively, and the projection objective 103 is coupled to a collimator lens 104Respectively, the Mueller matrices are MpAnd Mc。
The calibration method of the polarization aberration detection system of the immersion lithography machine is characterized by comprising the following steps:
the method comprises the following steps: the composite calibration method is used for calibrating the polarization aberration detection system of the immersion lithography machine by combining a Fourier analysis method and an eigenvalue calibration method;
the Fourier analysis method is used for calibrating the PSG and PSA to obtain their instrument matrixes G and A, and then the eigenvalue calibration method and the matrix operation are combined to calibrate the polarization aberration M of the collimator lens coupled with the projection objective lenscAt the same time, the polarization aberration M of the projection objective can be accurately obtainedp。
1.1, Fourier analysis is used for calibrating the polarization state generator PSG and the polarization state analyzer PSA, and instrument matrixes G and A are obtained. The method comprises the following specific steps:
1.1.1 rotating the wave plates in the polarization state generator PSG and the polarization state analyzer PSA to air, wherein the ratio of the rotation angle of the wide-angle quarter-wave plate in the polarization state generator PSG to the rotation angle of the quarter-wave plate in the polarization state analyzer PSA is 1: 5;
first, the fast axis azimuth error ε of the sum of the waveplates in the PSG and PSA is determined1And ε2Error of retardation epsilon4And ε5And the transmission axis azimuth angle error epsilon of the polarizing prism in the polarization state analyzer PSA3(ii) a The instrument matrices G and a used to solve the polarization state generator PSG and the polarization state analyzer PSA;
let us say that the retardation of the wide-angle quarter-wave plate in the polarization state generator PSG is delta1Retardation of the quarter-wave plate in the polarization analyzer PSA is delta2The following formula:
from equation (2), the polarization state generator PSG and polarization state analyzer PS can be obtainedError of devices in A, i.e. fast axis azimuth error ε of wave plates in polarization state generator PSG and polarization state analyzer PSA1And ε2Error of retardation epsilon4And ε5And the transmission axis azimuth angle error epsilon of the polarizing prism in the polarization state analyzer PSA3。
Secondly, the calculated errors are brought into the instrument matrixes G and A of the polarization state generator PSG and the polarization state analyzer PSA, so that the calibration of the polarization state generator PSG and the polarization state analyzer PSA is completed, and the instrument matrixes G and A of the polarization state generator PSG and the polarization state analyzer PSA are obtained.
Step two, solving instrument matrixes G and A of the polarization state generator PSG and the polarization state analyzer PSA by a method different from the method in the step one, namely calibrating the polarization aberration detection system of the immersion lithography machine by using a multi-step eigenvalue calibration method to obtain the instrument matrixes G and A;
and respectively placing the calibration sample S between the polarization state generator PSG and the projection objective lens and between the collimating lens and the polarization state analyzer PSA, respectively carrying out an eigenvalue calibration method, and then solving the instrument matrixes G and A according to matrix operation.
The method comprises the following specific steps:
2.1: placing a calibration sample S between a polarization state generator PSG and a projection objective, wherein the polarization state generator PSG is used as a group, and the instrument matrix is M21; the projection objective, the collimator, and the polarization analyzer PSA are a set, and the instrument matrix is M22, where M21 and M22 can be expressed as:
M21＝G, (7)
M22＝A·Mc·Mp. (8)
an eigenvalue calibration is performed once to obtain M21 and M22.
2.2: placing a calibration sample S between a collimating mirror and a polarization state analyzer PSA, wherein a polarization state generator PSG, a projection objective and the collimating mirror are used as a group, and the instrument matrix is M23; the polarization state analyzer PSA is used as a group, and its instrument matrix is M24, where M23 and M24 can be expressed as:
M23＝Mc·Mp·G, (9)
M24＝A. (10)
again, eigenvalue calibration is performed, and from equations (7) and (10), the instrument matrices G and a of the polarization state generator PSG and polarization state analyzer can be obtained by matrices M21 and M24.
Substituting the result of the step one or the step two into the step three to finish the calibration of the collimating mirror, namely obtaining the Mueller matrix M of the collimating mirrorcFinally, the polarization phase difference M of the projection objective is accurately obtainedp。
The third step comprises the following specific steps:
3.1 Place the calibration sample S between the projection objective and the collimator lens to perform eigenvalue calibration, in this process, set the polarization state generator PSG and the projection objective as one set, and set its instrument matrix as M11, and set the collimator lens and the polarization state analyzer PSA as the other set, and set its instrument matrix as M12. Then M11 and M12 can be expressed as:
M11＝Mp·G, (3)
M12＝A·Mc. (4)
by the eigenvalue calibration method, M11 and M12 can be obtained.
3.2 combining the PSG obtained in the first step or the second step with the instrument matrixes G and A of the PSA, and obtaining M through matrix operationpAnd McAs shown in the following formula:
Mp＝M11·G-1, (5)
Mc＝A-1·M12. (6)
the calibration of the polarization aberration detection system of the immersion lithography machine is completed, namely instrument matrixes G and A of a polarization state generator PSG and a polarization state analyzer PSA and a Mueller matrix M of a collimating mirror are obtainedcFinally, the polarization phase difference M of the projection objective is accurately obtainedp。
In general, the calibration sample S is selected from the best reference samples given in the prior publications: air, a polaroid with the transmission axis direction being the horizontal direction, a polaroid with the transmission axis direction being the vertical direction and a quarter wave plate with the fast axis azimuth angle being 30 degrees; but of note in the present invention are: the calibration samples in the third step are air, a polaroid and a wide-angle quarter-wave plate; and the calibration samples in step two, namely the air, the polaroid and the wide-angle quarter-wave plate in step 2.1, and the calibration samples in step 2.2, namely the air, the polaroid and the conventional quarter-wave plate.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. A calibration method of a polarization aberration detection system of an immersion lithography machine is characterized by comprising the following steps: the polarization aberration detection system of the immersion lithography machine mainly comprises an illuminating device, a polarization state generator PSG, a projection objective, a collimating lens coupled with the projection objective, a polarization state analyzer PSA and a CCD detector; the PSG consists of a polarizer and a wide-angle quarter-wave plate, and the PSA consists of a traditional quarter-wave plate and a polarizing prism;
the calibration method of the immersion lithography machine polarization aberration detection system comprises the following steps:
firstly, calibrating a polarization aberration detection system of an immersion lithography machine by using a composite calibration method by combining a Fourier analysis method and an eigenvalue calibration method;
1.1, a Fourier analysis method is used for calibrating a polarization state generator PSG and a polarization state analyzer PSA, obtaining instrument matrixes G and A, and obtaining a wave plate and fast axis azimuth angle error epsilon in the polarization state generator PSG and the polarization state analyzer PSA through obtaining1And ε2Error of retardation epsilon4And ε5And analysis of polarization stateLight transmission axis azimuth angle error epsilon of polarizing prism in PSA (pressure swing adsorption) device3(ii) a The instrument matrices G and a used to solve the polarization state generator PSG and the polarization state analyzer PSA;
1.2, bringing the obtained errors into instrument matrixes G and A of a polarization state generator PSG and a polarization state analyzer PSA, and completing the calibration of the polarization state generator PSG and the polarization state analyzer PSA to obtain the instrument matrixes G and A of the polarization state generator PSG and the polarization state analyzer PSA;
step two, solving instrument matrixes G and A of the polarization state generator PSG and the polarization state analyzer PSA by a method different from the method in the step one, namely calibrating the polarization aberration detection system of the immersion lithography machine by using a multi-step eigenvalue calibration method to obtain the instrument matrixes G and A;
respectively placing a calibration sample S between a polarization state generator PSG and a projection objective lens and between a collimating mirror and a polarization state analyzer PSA, respectively carrying out an eigenvalue calibration method, and then solving instrument matrixes G and A according to matrix operation;
substituting the result of the step one or the step two into the step three to finish the calibration of the collimating mirror, namely obtaining the Mueller matrix M of the collimating mirrorcFinally, the polarization phase difference M of the projection objective is accurately obtainedp；
The third step comprises the following specific steps:
3.1 placing the calibration sample S between the projection objective and the collimator lens for eigenvalue calibration, in this process, taking the polarization state generator PSG and the projection objective as one set, and setting the instrument matrix as M11, and taking the collimator lens and the polarization state analyzer PSA as another set, and setting the instrument matrix as M12, then M11 and M12 can be expressed as:
M11＝Mp·G (3)
M12＝A·Mc (4)
obtaining M11 and M12 by an eigenvalue calibration method;
3.2 combining the PSG obtained in the first step or the second step with the instrument matrixes G and A of the PSA, and obtaining M through matrix operationpAnd McAs shown in the following formula:
Mp＝M11·G-1 (5)
Mc＝A-1·M12 (6)
the calibration of the polarization aberration detection system of the immersion lithography machine is completed, namely instrument matrixes G and A of a polarization state generator PSG and a polarization state analyzer PSA and a Mueller matrix M of a collimating mirror are obtainedcFinally, the polarization phase difference M of the projection objective is accurately obtainedp。
2. The calibration method of the polarization aberration detection system of the immersion lithography machine according to claim 1, wherein the specific steps in the first step are as follows:
1.1, rotating the wave plate in the polarization state generator PSG and the polarization state analyzer PSA to measure the air, wherein the ratio of the rotation angle of the wide-angle quarter-wave plate in the polarization state generator PSG to the rotation angle of the quarter-wave plate in the polarization state analyzer PSA is 1: 5;
1.2, wherein the retardation of the wide-angle quarter-wave plate in the polarization state generator PSG is delta1Retardation of the quarter-wave plate in the polarization analyzer PSA is delta2The following formula:
the errors of the devices in the PSG and PSA, i.e. the fast axis azimuth angle errors ε of the wave plates in the PSG and PSA, are obtained according to equation (2)1And ε2Error of retardation epsilon4And ε5And the transmission axis azimuth angle error epsilon of the polarizing prism in the polarization state analyzer PSA3；
3. The calibration method of the polarization aberration detection system of the immersion lithography machine according to claim 1, wherein the specific steps in the second step are as follows:
2.1, placing a calibration sample S between a polarization state generator PSG and a projection objective, wherein the polarization state generator PSG is used as a group, and the instrument matrix is M21; the projection objective, the collimator, and the polarization analyzer PSA are a set, and the instrument matrix is M22, where M21 and M22 can be expressed as:
M21＝G (7)
M22＝A·Mc·Mp (8)
carrying out one-time eigenvalue calibration to obtain M21 and M22;
2.2, placing the calibration sample S between a collimating mirror and a polarization state analyzer PSA, wherein a polarization state generator PSG, a projection objective and the collimating mirror are used as a group, and the instrument matrix is M23; the polarization state analyzer PSA is used as a group, and its instrument matrix is M24, where M23 and M24 are expressed as:
M23＝Mc·Mp·G (9)
M24＝A (10)
again, eigenvalue calibration is performed, and the instrument matrices G and a of the polarization state generator PSG and polarization state analyzer are obtained from equations (7) and (10) by matrices M21 and M24.
4. The calibration method of the polarization aberration detection system of an immersion lithography machine according to claim 3, wherein the calibration samples in step three are air, a polarizer and a wide-angle quarter-wave plate; and the calibration samples in step two, namely the air, the polaroid and the wide-angle quarter-wave plate in step 2.1, and the calibration samples in step 2.2, namely the air, the polaroid and the conventional quarter-wave plate.
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| CN104535192A (en) * | 2015-01-09 | 2015-04-22 | 北京理工大学 | Stokes polarization meter error calibration and compensation method based on wave plate rotating method |
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