CN101949734B

CN101949734B - method for improving measurement precision of light beam polarization degree

Info

Publication number: CN101949734B
Application number: CN201010259354XA
Authority: CN
Inventors: 李中梁; 王向朝; 唐锋
Original assignee: Shanghai Institute of Optics and Fine Mechanics of CAS
Current assignee: Beijing Guowang Optical Technology Co Ltd
Priority date: 2010-08-20
Filing date: 2010-08-20
Publication date: 2011-11-09
Anticipated expiration: 2030-08-20
Also published as: CN101949734A

Abstract

A method to improve the accuracy of beam polarization measurement. The polarization detection device used includes a phase delay device, a polarizer and a photodetector arranged sequentially along the optical axis of the device system. The output of the photodetector is connected to a signal processing system to be measured. The light beam is incident on the phase delay device and analyzer parallel to the optical axis of the system, and is detected by the photodetector. The electrical signal output by the photodetector is sent to the signal processing system for data processing. The characteristic is that, according to the polarization direction of the light beam to be measured, the direction of the transmission axis of the analyzer is adjusted to be parallel or perpendicular to the polarization direction of the light beam to be measured, and then the polarization degree of the light beam to be measured is determined. Measurement. According to the light intensity detected by the photodetector, the Stokes parameters and polarization degree of the beam to be measured are obtained. The invention can improve the measurement accuracy of polarization degree.

Description

The Method of Improving the Measuring Accuracy of Beam Polarization Degree

技术领域 technical field

本发明涉及光束偏振度的检测，特别是一种提高光束偏振度测量精度的方法。The invention relates to the detection of the degree of polarization of light beams, in particular to a method for improving the measurement accuracy of the degree of polarization of light beams.

背景技术 Background technique

半导体制造技术的进步总是以曝光波长的减小、投影物镜数值孔径的增大以及光刻工艺因子k1的缩小为动力的。最近几年，浸没式光刻技术取得了快速发展。在浸没式光刻技术中，采用某种液体填充在物镜最后一片镜片和硅片上的光刻胶之间，使得投影物镜的数值孔径得到显著提高。当光刻机投影物镜的数值孔径接近0.8或者更大时，照明光的偏振对光刻成像的影响已不可忽视。采用合适的偏振光照明是一种在大数值孔径情况下提高成像对比度的有力方法。对于不同照明方式，偏振照明要求具有不同的线偏振方向的偏振光，如x方向偏振光、y方向偏振光、径向偏振光、切向偏振光等。The progress of semiconductor manufacturing technology is always driven by the reduction of exposure wavelength, the increase of numerical aperture of projection objective lens and the reduction of lithography process factor k1. In recent years, immersion lithography technology has achieved rapid development. In immersion lithography technology, a certain liquid is used to fill between the last lens of the objective lens and the photoresist on the silicon wafer, so that the numerical aperture of the projection objective lens is significantly improved. When the numerical aperture of the projection objective lens of the lithography machine is close to 0.8 or larger, the influence of the polarization of the illumination light on the lithography imaging can no longer be ignored. Using properly polarized illumination is a powerful way to improve imaging contrast at large numerical apertures. For different lighting methods, polarized lighting requires polarized light with different linear polarization directions, such as x-direction polarized light, y-directed polarized light, radially polarized light, tangentially polarized light, and the like.

当使用偏振光照明时，光刻机的照明系统中存在诸多因素会影响光的偏振态。最主要的是光学材料的本征双折射和应力双折射使光的偏振度降低。此外，光学薄膜的偏振特性，光在界面的反射和折射也会影响光的偏振。因此，在偏振光照明系统中，由于偏振控制的需要，应实时检测照明光的偏振信息，并反馈控制照明系统中的旋转波片，保证具有高偏振度的线偏振光输出。此外，还需要进行偏振照明检测以用于光刻机的装校和维护。在先技术1(日本专利：特開2005-005521)提出了一种利用旋转相位延迟器法的偏振参数检测装置。图2为在先技术1提出的投影曝光装置中照明光瞳偏振参数检测装置的示意图。由图2可知，该偏振参数检测装置包括针孔掩模10、变换透镜组20、相位延迟器件2及其驱动器6、检偏器3、光电探测器4和信号处理系统5。照明光束通过针孔掩模10上的针孔101后，经变换透镜组20成为平行光束。该平行光束作为待测光束1，依次通过相位延迟器件2和检偏器3后由光电探测器4探测。When using polarized light illumination, there are many factors in the illumination system of the lithography machine that will affect the polarization state of the light. The most important thing is that the intrinsic birefringence and stress birefringence of optical materials reduce the degree of polarization of light. In addition, the polarization characteristics of optical films, the reflection and refraction of light at the interface will also affect the polarization of light. Therefore, in the polarized light illumination system, due to the need for polarization control, the polarization information of the illumination light should be detected in real time, and the rotating waveplate in the illumination system should be feedback-controlled to ensure the output of linearly polarized light with a high degree of polarization. In addition, polarized illumination detection is also required for calibration and maintenance of lithography machines. Prior Art 1 (Japanese Patent: Japanese Patent Laid-Open No. 2005-005521) proposes a polarization parameter detection device using a rotational phase retarder method. FIG. 2 is a schematic diagram of an illumination pupil polarization parameter detection device in the projection exposure device proposed in prior art 1. FIG. As can be seen from FIG. 2 , the polarization parameter detection device includes a pinhole mask 10 , a transformation lens group 20 , a phase delay device 2 and its driver 6 , an analyzer 3 , a photodetector 4 and a signal processing system 5 . After the illumination beam passes through the pinhole 101 on the pinhole mask 10 , it becomes a parallel beam through the conversion lens group 20 . The parallel light beam is used as the light beam 1 to be measured, and is detected by the photodetector 4 after passing through the phase delay device 2 and the polarizer 3 in sequence.

所述的针孔掩模10置于投影曝光装置的掩模面或附近，或者与掩模面共轭的平面或附近(或硅片面或附近，或者与硅片面共轭的平面或附近)。The pinhole mask 10 is placed on or near the mask surface of the projection exposure device, or on or near a plane conjugate to the mask surface (or on or near the silicon wafer surface, or on or near the plane conjugate to the silicon wafer surface) ).

利用在先技术1中的装置进行测量时，相位延迟器件2绕装置的系统光轴旋转，利用在先技术1和在先技术2(日本专利：特開2006-179660)中的数据处理方法对光电探测器输出的电信号进行处理，可以得到待测光束的斯托克斯参数和偏振度。但该装置所需的相位延迟器件和检偏器均工作在深紫外波段，在此波段难以按照设计指标制造理想的器件，因此产生斯托克斯参数和偏振度测量误差。When using the device in the prior art 1 to measure, the phase delay device 2 rotates around the system optical axis of the device, and the data processing method in the prior art 1 and the prior art 2 (Japanese patent: Japanese Patent Laid-Open No. 2006-179660) is used to The electrical signal output by the photodetector is processed to obtain the Stokes parameter and polarization degree of the beam to be measured. However, the phase delay device and polarizer required by the device all work in the deep ultraviolet band, and it is difficult to manufacture ideal devices in this band according to the design specifications, so errors in Stokes parameter and polarization degree measurement occur.

为此，在先技术2提出了不受相位延迟器件和检偏器相关误差的影响、高精度的测量偏振态分布的方法。该方法是在用相位延迟器件和检偏器构成偏振检测装置之前测量各器件的偏振特性，包括相位延迟器件相位延迟量的面内分布、快轴方向和检偏器的透光轴方向、消光比分布等。但该方法不能测量构成偏振检测装置后相位延迟器件的快轴方向和检偏器透光轴的方向的定位误差。因此，当偏振检测装置中存在相位延迟器件快轴定位误差、检偏器透光轴定位误差时，仍将影响偏振度的测量结果。For this reason, prior art 2 proposes a method for measuring the polarization state distribution with high precision, which is not affected by the relative errors of the phase delay device and the polarizer. The method is to measure the polarization characteristics of each device before using the phase delay device and the analyzer to form a polarization detection device, including the in-plane distribution of the phase delay of the phase delay device, the direction of the fast axis and the direction of the transmission axis of the analyzer, and the extinction than the distribution etc. However, this method cannot measure the positioning error between the fast axis direction of the phase delay device and the direction of the light transmission axis of the analyzer after the polarization detection device is formed. Therefore, when there is a positioning error of the fast axis of the phase delay device and the positioning error of the transmission axis of the analyzer in the polarization detection device, the measurement result of the degree of polarization will still be affected.

发明内容 Contents of the invention

为减小器件制造过程中产生的相位延迟器件的相位延迟量误差、快轴方向误差和检偏器的透光轴方向误差、消光比误差，以及构成偏振检测装置时相位延迟器件的快轴方向定位误差和检偏器的透光轴方向定位误差对偏振度测量的影响，本发明提出一种提高光束偏振度测量精度的方法。该方法通过调整检偏器透光轴的方向，可以有效减小相位延迟器件和检偏器的上述误差对偏振度测量结果的影响。In order to reduce the phase delay error of the phase delay device, the fast axis direction error, the transmittance axis direction error of the analyzer, the extinction ratio error, and the fast axis direction of the phase delay device when the polarization detection device is formed during the device manufacturing process In view of the influence of positioning error and positioning error of the light transmission axis direction of the analyzer on the measurement of the degree of polarization, the invention proposes a method for improving the measurement accuracy of the degree of polarization of the beam. By adjusting the direction of the light transmission axis of the analyzer, the method can effectively reduce the influence of the above-mentioned errors of the phase delay device and the analyzer on the measurement result of the degree of polarization.

本发明的技术解决方案如下：Technical solution of the present invention is as follows:

一种提高光束偏振度测量精度的方法，使用的偏振检测装置包括沿装置系统光轴依次设置的相位延迟器件、检偏器和光电探测器，该光电探测器的输出接信号处理系统，所述的相位延迟器件在驱动器的驱动下可绕装置系统光轴旋转，待测光束平行于系统光轴入射至所述的相位延迟器件和检偏器，并由所述的光电探测器探测，该光电探测器输出的电信号送入所述的信号处理系统进行数据处理，其特点在于，根据所述的待测光束的偏振方向，调整所述的检偏器的透光轴方向与所述的待测光束的偏振方向平行或垂直后，再进行待测光束的偏振度的测量。A method for improving the measurement accuracy of the degree of polarization of a light beam. The polarization detection device used includes a phase delay device, a polarizer, and a photodetector arranged sequentially along the optical axis of the device system, and the output of the photodetector is connected to a signal processing system. The phase delay device can rotate around the optical axis of the device system under the drive of the driver, and the light beam to be measured is incident on the phase delay device and the analyzer parallel to the system optical axis, and is detected by the photodetector. The electrical signal output by the detector is sent to the signal processing system for data processing, which is characterized in that, according to the polarization direction of the light beam to be measured, the direction of the transmission axis of the analyzer and the direction of the light transmission axis of the light beam to be measured are adjusted. After the polarization direction of the measuring beam is parallel or vertical, the polarization degree of the beam to be measured is measured.

当概知待测光束的偏振方向时，其具体测量步骤如下：When the polarization direction of the beam to be measured is generally known, the specific measurement steps are as follows:

①调整所述的检偏器的透光轴方向与所述的待测光束的偏振方向平行或垂直；① adjusting the direction of the transmission axis of the analyzer to be parallel or perpendicular to the polarization direction of the beam to be measured;

②利用所述的偏振检测装置对待测光束进行测量并经数据处理后，最终得到所述的待测光束的斯托克斯参数和偏振度。② Using the polarization detection device to measure the light beam to be measured and after data processing, finally obtain the Stokes parameter and degree of polarization of the light beam to be measured.

当未知待测光束的偏振方向时，其具体测量步骤如下：When the polarization direction of the beam to be measured is unknown, the specific measurement steps are as follows:

①利用所述的偏振检测装置按现有的方法测量并经数据处理后获得待测光束的第一次斯托克斯参数和待测光束的偏振方向；① Utilize the described polarization detection device to measure according to the existing method and obtain the first Stokes parameter of the beam to be measured and the polarization direction of the beam to be measured after data processing;

②调整所述的检偏器的透光轴方向与所述的待测光束的偏振方向平行或垂直；② Adjusting the direction of the transmission axis of the analyzer to be parallel or perpendicular to the polarization direction of the beam to be measured;

③利用所述的偏振检测装置对待测光束进行第二次测量并经数据处理后，最终得到所述的待测光束的斯托克斯参数和偏振度。③ Using the polarization detection device to measure the light beam to be measured for the second time and after data processing, finally obtain the Stokes parameter and degree of polarization of the light beam to be measured.

所述的相位延迟器件为产生90°相位延迟的四分之一波片、电光调制器或光弹调制器。The phase delay device is a quarter-wave plate, an electro-optic modulator or a photoelastic modulator that produces a 90° phase delay.

所述的驱动器驱动所述的相位延迟器件绕系统光轴匀速旋转，或者通过驱动相位延迟器件旋转能够设置相位延迟器件的快轴与所述的检偏器透光轴之间至少四个不同的角度的位置。The driver drives the phase delay device to rotate at a constant speed around the optical axis of the system, or by driving the phase delay device to rotate, at least four different positions between the fast axis of the phase delay device and the transmission axis of the analyzer can be set. angle position.

所述的光电探测器为二维面阵探测器或点探测器。The photodetectors are two-dimensional array detectors or point detectors.

根据所述的待测光束的偏振方位角，调整所述的检偏器的透光轴方向与所述的待测光束的偏振方向平行或垂直，可有效减小相位延迟器件和检偏器的制造误差、测量过程中各器件的角度定位误差对测量结果的影响。According to the polarization azimuth angle of the light beam to be measured, adjusting the transmission axis direction of the polarizer to be parallel or perpendicular to the polarization direction of the light beam to be measured can effectively reduce the phase retardation device and the polarizer. The influence of manufacturing errors and angular positioning errors of each device during the measurement process on the measurement results.

本发明由于采用了上述技术方案，与在先技术相比，具有以下优点和积极效果：Compared with the prior art, the present invention has the following advantages and positive effects due to the adoption of the above-mentioned technical solution:

1、由于在深紫外波段制造性能理想的相位延迟器件和检偏器较困难，相位延迟器件的延迟量、快轴方向和检偏器的透光轴方向、消光比等实际参数与设计参数之间的误差将影响偏振度的测量精度。利用本发明的光束偏振检测装置进行测量时，通过将检偏器的透光轴置于与待测光束偏振方向垂直或平行的方向，可有效减小上述制造误差对偏振度测量的影响。1. Since it is difficult to manufacture phase retardation devices and polarizers with ideal performance in the deep ultraviolet band, the actual parameters such as the retardation of the phase delay device, the fast axis direction, the transmittance axis direction of the polarizer, and the extinction ratio are different from the design parameters. The error between them will affect the measurement accuracy of the degree of polarization. When the beam polarization detection device of the present invention is used for measurement, by placing the light transmission axis of the polarizer in a direction perpendicular or parallel to the polarization direction of the beam to be measured, the influence of the above-mentioned manufacturing errors on the degree of polarization measurement can be effectively reduced.

2、在旋转相位延迟器件测量待测光束斯托克斯参数的过程中，相位延迟器件的初始快轴角度、检偏器的透光轴角度存在定位误差，将影响偏振度的测量精度，通过将调整检偏器的透光轴置于与待测光束偏振方向平行或垂直的方向，可有效减小上述定位误差对偏振度测量的影响。2. During the process of measuring the Stokes parameters of the beam to be measured by the rotating phase delay device, there are positioning errors in the initial fast axis angle of the phase delay device and the light transmission axis angle of the analyzer, which will affect the measurement accuracy of the degree of polarization. Adjusting the transmission axis of the polarizer in a direction parallel or perpendicular to the polarization direction of the beam to be measured can effectively reduce the influence of the above positioning error on the polarization degree measurement.

附图说明 Description of drawings

图1是本发明的提高光束偏振度测量精度的方法所使用的偏振检测装置示意图。FIG. 1 is a schematic diagram of a polarization detection device used in the method for improving the measurement accuracy of the beam polarization degree of the present invention.

图2是现有的投影曝光装置中照明光瞳偏振参数检测装置的示意图。FIG. 2 is a schematic diagram of an illumination pupil polarization parameter detection device in a conventional projection exposure device.

具体实施方式 Detailed ways

下面结合实施例和附图对本发明进行进一步说明，但不应以此限制本发明的保护范围。The present invention will be further described below in conjunction with the embodiments and accompanying drawings, but the protection scope of the present invention should not be limited thereby.

本发明提高光束偏振度测量精度的方法所使用的偏振检测装置的结构示意图如图1所示。由图1可知，本发明所使用的偏振检测装置包括沿装置系统光轴依次设置的相位延迟器件2、检偏器3和光电探测器4，该光电探测器4的输出接信号处理系统5，所述的相位延迟器件2在驱动器6的驱动下可绕装置系统光轴旋转，待测光束1平行于系统光轴入射至所述的相位延迟器件2和检偏器3，并由所述的光电探测器4探测，该光电探测器4输出的电信号送入所述的信号处理系统5进行数据处理。The structural schematic diagram of the polarization detection device used in the method for improving the measurement accuracy of the polarization degree of the beam of the present invention is shown in FIG. 1 . As can be seen from Fig. 1, the polarization detection device used in the present invention comprises a phase delay device 2, a polarizer 3 and a photodetector 4 arranged sequentially along the optical axis of the device system, and the output of the photodetector 4 is connected to a signal processing system 5, The phase delay device 2 can rotate around the optical axis of the device system under the drive of the driver 6, and the light beam 1 to be measured is incident on the phase delay device 2 and the polarizer 3 parallel to the system optical axis, and is transmitted by the The photodetector 4 detects, and the electrical signal output by the photodetector 4 is sent to the signal processing system 5 for data processing.

本发明提高光束偏振度测量精度的方法(本实施例为未知待测光束1的偏振方向)的具体测量步骤如下：The specific measurement steps of the method for improving the measurement accuracy of the beam polarization degree of the present invention (in this embodiment, the polarization direction of the unknown beam 1 to be measured) are as follows:

①利用所述的偏振检测装置按现有的方法测量并经数据处理后获得待测光束1的第一次斯托克斯参数和待测光束1的偏振方向；① Utilize the described polarization detection device to measure according to the existing method and obtain the first Stokes parameter of the beam 1 to be measured and the polarization direction of the beam 1 to be measured after data processing;

②调整所述的检偏器3的透光轴方向与所述的待测光束1的偏振方向平行或垂直；② Adjust the direction of the transmission axis of the analyzer 3 to be parallel or perpendicular to the polarization direction of the light beam 1 to be measured;

③利用所述的偏振检测装置对待测光束1进行第二次测量并经数据处理后，最终得到所述的待测光束1的斯托克斯参数和偏振度。③ Using the polarization detection device to measure the light beam 1 to be measured for the second time and after data processing, finally obtain the Stokes parameter and the degree of polarization of the light beam 1 to be measured.

所述的相位延迟器件2为产生90°相位延迟的四分之一波片、电光调制器或光弹调制器。在本实施例中相位延迟器件2为四分之一波片。The phase delay device 2 is a quarter-wave plate, an electro-optic modulator or a photoelastic modulator that generates a 90° phase delay. In this embodiment, the phase delay device 2 is a quarter-wave plate.

所述的驱动器6可驱动相位延迟器件2绕系统光轴匀速旋转，或者通过驱动相位延迟器件2旋转能够设置至少四个不同的相位延迟器件2的快轴与检偏器3透光轴之间的角度。本实施例中驱动器6可驱动相位延迟器件2绕系统光轴匀速旋转。The driver 6 can drive the phase delay device 2 to rotate at a constant speed around the optical axis of the system, or at least four different phase delay devices 2 can be set between the fast axis of the phase delay device 2 and the light transmission axis of the analyzer 3 by driving the phase delay device 2 to rotate Angle. In this embodiment, the driver 6 can drive the phase delay device 2 to rotate around the optical axis of the system at a constant speed.

所述的检偏器3在理想情况下对于特定方向的线偏振光的透过率为100％，该方向为检偏器3的透光轴方向；而与该特定方向垂直的线偏振光的透过率为0。定义平行于透光轴方向和垂直于透光轴方向的线偏振光的强度透过率之比为消光系数p，理想情况下p为无穷大。在本实施例中检偏器3为偏振棱镜。The transmittance of the described analyzer 3 for linearly polarized light in a specific direction is ideally 100%, and this direction is the light transmission axis direction of the analyzer 3; and the transmittance of the linearly polarized light perpendicular to the specific direction is The transmittance is 0. Define the ratio of the intensity transmittance of linearly polarized light parallel to the direction of the light transmission axis and perpendicular to the direction of the light transmission axis as the extinction coefficient p, ideally p is infinite. In this embodiment, the analyzer 3 is a polarizing prism.

所述的相位延迟器件2和检偏器3的制造误差包括相位延迟器件2的相位延迟量误差、快轴方向误差和检偏器3的透光轴方向误差、消光比误差；所述的测量过程中相位延迟器件2和检偏器3的角度定位误差包括相位延迟器件2的初始快轴方向定位误差和检偏器3的透光轴方向定位误差。The manufacturing errors of the phase delay device 2 and the polarizer 3 include the phase delay error of the phase delay device 2, the fast axis direction error and the transmission axis direction error and the extinction ratio error of the polarizer 3; the measurement The angular positioning error of the phase delay device 2 and the polarizer 3 during the process includes the initial fast axis direction positioning error of the phase delay device 2 and the light transmission axis direction positioning error of the polarizer 3 .

所述的光电探测器4为二维面阵探测器或点探测器。本实施例中光电探测器4为二维面阵CCD，以测量光束的偏振度分布。The photodetector 4 is a two-dimensional array detector or a point detector. In this embodiment, the photodetector 4 is a two-dimensional area array CCD to measure the polarization distribution of the light beam.

所述的信号处理系统5利用在先技术1和在先技术2中的数据处理方法对光电探测器输出的电信号进行处理，得到待测光束1的斯托克斯参数和偏振度。The signal processing system 5 uses the data processing methods in the prior art 1 and the prior art 2 to process the electrical signal output by the photodetector to obtain the Stokes parameter and the degree of polarization of the beam 1 to be measured.

定义图1中所示的xyz坐标系，其中z轴为偏转检测装置系统光轴方向，xy平面为与系统光轴垂直的平面。设待测光束1的斯托克斯矢量为S＝[S₀，S₁，S₂，S₃]^T(右上角“T”表示矩阵转置)，其偏振度为：Define the xyz coordinate system shown in Figure 1, where the z-axis is the direction of the optical axis of the deflection detection device system, and the xy plane is a plane perpendicular to the optical axis of the system. Assuming the Stokes vector of beam 1 to be measured is S=[S ₀ , S ₁ , S ₂ , S ₃ ] ^T ("T" in the upper right corner represents matrix transposition), its degree of polarization is:

$V V = = \sqrt{\frac{{S S}_{11}^{22} + + {S S}_{22}^{22} + + {S S}_{33}^{22}}{{S S}_{00}^{22}}} . . - - - - - - ((11))$

对于线偏振光，偏振度V是表征该线偏振光的偏振特性的重要参数。For linearly polarized light, the degree of polarization V is an important parameter to characterize the polarization characteristics of the linearly polarized light.

定义线偏振光偏振方向与x轴正方向之间的角度为偏振方位角

其范围为

定义四分之一波片快轴与x轴正方向之间的角度为快轴角度θ，其范围为-90°≤θ≤90°；定义偏振棱镜透光轴与x轴正方向之间的角度为透光轴角度α，其范围为-90°≤α≤90°。Define the angle between the polarization direction of linearly polarized light and the positive direction of the x-axis as the polarization azimuth angle

its range is

Define the angle between the fast axis of the quarter-wave plate and the positive direction of the x-axis as the fast axis angle θ, and its range is -90°≤θ≤90°; define the angle between the transmission axis of the polarizing prism and the positive direction of the x-axis The angle is the transmission axis angle α, and its range is -90°≤α≤90°.

所述的绕偏振检测装置的系统光轴旋转的四分之一波片的穆勒矩阵为：The Mueller matrix of the quarter-wave plate that rotates around the system optical axis of the polarization detection device is:

$M m ((θ θ)) = = [\begin{matrix} 11,, & 00,, & 00,, & 00 \\ 00,, & {cos cos}^{22} 22 θ θ + + {sin sin}^{22} 22 θ θ cos cos δ δ,, & sin sin 22 θ θ cos cos 22 θ θ - - sin sin 22 θ θ cos cos 22 θ θ cos cos δ δ,, & - - sin sin 22 θ θ sin sin δ δ \\ 00,, & sin sin 22 θ θ cos cos 22 θ θ - - sin sin 22 θ θ cos cos 22 θ θ cos cos δ δ,, & {sin sin}^{22} 22 θ θ + + {cos cos}^{22} 22 θ θ cos cos δ δ,, & cos cos 22 θ θ sin sin δ δ \\ 00,, & sin sin 22 θ θ sin sin δ δ,, & - - cos cos 22 θ θ sin sin δ δ,, & cos cos δ δ \end{matrix}],, - - - - - - ((22))$

其中，δ为四分之一波片的相位延迟量，理想情况下δ＝π/2。Wherein, δ is the phase delay of the quarter-wave plate, ideally δ=π/2.

透光轴角度为α的偏振棱镜的穆勒矩阵为：The Mueller matrix of a polarizing prism with a transmission axis angle of α is:

$P P ((α α)) = = [\begin{matrix} 11,, & \frac{p p - - 11}{p p + + 11} cos cos 22 α α,, & \frac{p p - - 11}{p p + + 11} sin sin 22 α α,, & 00 \\ \frac{p p - - 11}{p p + + 11} cos cos 22 α α,, & {cos cos}^{22} 22 α α + + \frac{22 \sqrt{p p}}{p p + + 11} {sin sin}^{22} 22 α α,, & sin sin 22 α α cos cos 22 α α - - \frac{22 \sqrt{p p}}{p p + + 11} sin sin 22 α α cos cos 22 α α,, & 00 \\ \frac{p p - - 11}{p p + + 11} sin sin 22 α α,, & sin sin 22 α α cos cos 22 α α - - \frac{22 \sqrt{p p}}{p p + + 11} sin sin 22 α α cos cos 22 α α,, & {sin sin}^{22} 22 α α + + \frac{22 \sqrt{p p}}{p p + + 11} {cos cos}^{22} 22 α α,, & 00 \\ 00,, & 00,, & 00,, & \frac{22 \sqrt{p p}}{p p + + 11} \end{matrix}] . . - - - - - - ((33))$

待测光束1经过四分之一波片和偏振棱镜后，斯托克斯矢量为S′＝P(α)M(θ)S。由于斯托克斯矢量的第一行表示光波的总强度，光电探测器4能够探测到的光强即为此强度值，所以此处只关心斯托克斯矢量的第一行数值。本实施例中光电探测器4为面阵CCD，它的每个像素均得到光强相关的数据，对每个像素的数据进行处理得到该像素处待测光束1的斯托克斯参数。为了便于理解，现以一个像素为例进行说明。After the beam 1 to be measured passes through the quarter-wave plate and the polarizing prism, the Stokes vector is S'=P(α)M(θ)S. Since the first line of the Stokes vector represents the total intensity of the light wave, the light intensity that can be detected by the photodetector 4 is this intensity value, so only the value of the first line of the Stokes vector is concerned here. In this embodiment, the photodetector 4 is an area array CCD, and each pixel of it obtains data related to light intensity, and the data of each pixel is processed to obtain the Stokes parameter of the beam 1 to be measured at the pixel. For ease of understanding, a pixel is taken as an example for description.

在理想情况下，即＝π/2、p为无穷大时，有：In an ideal case, that is, when =π/2, p is infinite, there are:

S₀′(θ)＝S₀+S₁[cos2αcos²2θ+sin2αsin2θcos2θ]， (4)S ₀ ′(θ)＝S ₀ +S ₁ [cos2αcos ² 2θ+sin2αsin2θcos2θ], (4)

+S₂[cos2αsin2θcos2θ+sin2αsin²2θ]+S₃(sin2αcos2θ-cos2αsin2θ)+S ₂ [cos2αsin2θcos2θ+sin2αsin ² 2θ]+S ₃ (sin2αcos2θ-cos2αsin2θ)

测量时，转动四分之一波片改变θ。将S₀’作为θ的函数，并将其进行傅立叶展开：During the measurement, turning the quarter-wave plate changes θ. Taking S ₀ ' as a function of θ, and Fourier expanding it:

${S S}_{00}^{' '} ((θ θ)) = = \frac{{a a}_{00}}{22} + + \underset{n no}{Σ Σ} (({a a}_{n no} cos cos nθ nθ + + {b b}_{n no} sin sin nθ nθ)),, - - - - - - ((55))$

为由S₀’(θ)得到系数a_n和b_n，可以使用下式：To obtain the coefficients a _n and b _n from S ₀ '(θ), the following formula can be used:

${a a}_{n no} = = \frac{11}{π π} {&Integral; &Integral;}_{- - π π}^{π π} {S S}_{00}^{' '} ((θ θ)) cos cos nθdθ nθdθ,, - - - - - - ((66))$

${b b}_{n no} = = \frac{11}{π π} {&Integral; &Integral;}_{- - π π}^{π π} {S S}_{00}^{' '} ((θ θ)) sin sin nθdθ nθdθ . . - - - - - - ((77))$

这样分别得到如下列式(8)-(12)所示的a₀、a₂、b₂、a₄和b₄：In this way, a ₀ , a ₂ , b ₂ , a ₄ and b ₄ are respectively obtained as shown in the following formulas (8)-(12):

$\frac{{a a}_{00}}{22} = = {S S}_{00} + + \frac{p p - - 11}{22 ((p p + + 11))} (({S S}_{11} cos cos 22 α α + + {S S}_{22} sin sin 22 α α)),, - - - - - - ((88))$

${a a}_{22} = = \frac{p p - - 11}{p p + + 11} {S S}_{33} sin sin 22 α α,, - - - - - - ((99))$

${b b}_{22} = = - - \frac{p p - - 11}{p p + + 11} {S S}_{33} cos cos 22 α α,, - - - - - - ((1010))$

${a a}_{44} = = \frac{p p - - 11}{22 ((p p + + 11))} (({S S}_{11} cos cos 22 α α - - {S S}_{22} sin sin 22 α α)),, - - - - - - ((1111))$

${b b}_{44} = = \frac{p p - - 11}{22 ((p p + + 11))} (({S S}_{11} sin sin 22 α α + + {S S}_{22} cos cos 22 α α)) . . - - - - - - ((1212))$

利用得到的a₀、a₂、b₂、a₄和b₄，可以计算得到与待测光束1的偏振态对应的4个斯托克斯参数S₀、S₁、S₂、S₃：Using the obtained a ₀ , a ₂ , b ₂ , a ₄ and b ₄ , the four Stokes parameters S ₀ , S ₁ , S ₂ , and S ₃ corresponding to the polarization state of the beam 1 to be measured can be calculated:

${S S}_{00} = = \frac{{a a}_{00}}{22} - - (({a a}_{44} cos cos 44 α α + + {b b}_{44} sin sin 44 α α)),, - - - - - - ((1313))$

${S S}_{11} = = \frac{22 ((p p + + 11))}{((p p - - 11))} (({a a}_{44} cos cos 22 α α + + {b b}_{44} sin sin 22 α α)),, - - - - - - ((1414))$

${S S}_{22} = = \frac{22 ((p p + + 11))}{((p p - - 11))} (({b b}_{44} cos cos 22 α α + + {a a}_{44} sin sin 22 α α)),, - - - - - - ((1515))$

${S S}_{33} = = \frac{- - ((p p + + 11)) {b b}_{22}}{((p p - - 11)) cos cos 22 α α} = = \frac{((p p + + 11)) {a a}_{22}}{((p p - - 11)) sin sin 22 α α} . . - - - - - - ((1616))$

但在实际测量时，由于在器件制造和测量过程中可能存在各种误差，如四分之一波片的快轴角度误差、相位延迟量误差和偏振棱镜透光轴角度误差、消光比误差等，此时得到的关于S₀、S₁、S₂、S₃的四元一次方程组为：However, in the actual measurement, various errors may exist in the process of device manufacturing and measurement, such as the fast axis angle error of the quarter-wave plate, the phase delay error, the polarizing prism transmission axis angle error, and the extinction ratio error. , the obtained quaternary linear equations about S ₀ , S ₁ , S ₂ , and S ₃ are:

${S S}_{00}^{' '} ((θ θ)) = =$

${S S}_{00} + + {S S}_{11} \frac{p p - - 11}{p p + + 11} {{cos cos 22 ((α α + + Δα Δα)) + + [[{cos cos}^{22} 22 ((θ θ + + Δθ Δθ)) + + {sin sin}^{22} 22 ((θ θ + + Δθ Δθ)) cos cos δ δ]] + + sin sin 22 ((α α + + Δα Δα)) sin sin 22 ((θ θ + + Δθ Δθ)) cos cos 22 ((θ θ + + Δθ Δθ)) ((11 - - cos cos δ δ))}}$

$+ + {S S}_{22} \frac{p p - - 11}{p p + + 11} {{cos cos 22 ((α α + + Δα Δα)) sin sin 22 ((θ θ + + Δθ Δθ)) cos cos 22 ((θ θ + + Δθ Δθ)) ((11 - - cos cos δ δ)) + + sin sin 22 ((α α + + Δα Δα)) [[{sin sin}^{22} 22 ((θ θ + + Δθ Δθ)) + + {cos cos}^{22} 22 ((θ θ + + Δθ Δθ)) cos cos δ δ]]}}$

$+ + {S S}_{33} \frac{p p - - 11}{p p + + 11} [[sin sin 22 ((α α + + Δα Δα)) cos cos 22 ((θ θ + + Δθ Δθ)) - - cos cos 22 ((α α + + Δα Δα)) sin sin 22 ((θ θ + + Δθ Δθ))]] sin sin δ δ,, - - - - - - ((1717))$

其中：Δα为偏振棱镜透光轴的角度误差，Δθ为四分之一波片的初始(即四分之一波片未转动时的初始状态)快轴角度误差。Among them: Δα is the angular error of the transmission axis of the polarizing prism, and Δθ is the initial fast axis angle error of the quarter-wave plate (that is, the initial state when the quarter-wave plate is not rotated).

当存在上述误差时，CCD的一个像素实际探测到的光强由(17)式表示，而计算斯托克斯参数S₀、S₁、S₂、S₃时使用的光强为(4)式，从而导致得到的斯托克斯参数存在误差，影响偏振度V的计算结果。When the above errors exist, the light intensity actually detected by one pixel of the CCD is expressed by formula (17), and the light intensity used to calculate the Stokes parameters S ₀ , S ₁ , S ₂ , and S ₃ is (4) formula, resulting in errors in the obtained Stokes parameters, which affect the calculation results of the degree of polarization V.

我们仿真了在不同误差条件下偏振度V的误差。We simulated the error of the degree of polarization V under different error conditions.

对于线偏振光，当四分之一波片的快轴角度θ存在误差Δθ＝1°时，偏振度V的误差ΔV随偏振棱镜的透光轴角度α和待测光束1的偏振方位角

的变化如表1所示。由表1可知，当偏振棱镜的透光轴角度α和待测光束1的偏振方位角

之间满足

或

(α≤0)或

(α＞0)时，偏振度V的误差为0。而当偏振棱镜的透光轴方向与待测光束1的偏振方向平行

或垂直(

或-90°)时，偏振度V的误差的绝对值为0.001，可以忽略。对于线偏振光，当偏振棱镜的透光轴角度α存在误差Δα＝1°时，偏振度V的误差ΔV随偏振棱镜的透光轴角度α和待测光束1的偏振方位角

的变化如表2所示。由表2可知，当偏振棱镜的透光轴方向与待测光束1的偏振方向平行

或垂直(或-90°)时，偏振度V的误差为0。For linearly polarized light, when there is an error Δθ=1° in the fast axis angle θ of the quarter-wave plate, the error ΔV of the degree of polarization V varies with the transmission axis angle α of the polarizing prism and the polarization azimuth angle of the beam 1 to be measured

The changes are shown in Table 1. It can be seen from Table 1 that when the angle α of the transmission axis of the polarizing prism and the polarization azimuth angle of the beam 1 to be measured

meet between

or

(α≤0) or

When (α>0), the error of the degree of polarization V is 0. And when the direction of the transmission axis of the polarizing prism is parallel to the polarization direction of the beam 1 to be measured

or vertically (

or -90°), the absolute value of the error of the degree of polarization V is 0.001, which can be ignored. For linearly polarized light, when there is an error Δα=1° in the transmission axis angle α of the polarizing prism, the error ΔV of the degree of polarization V varies with the transmission axis angle α of the polarizing prism and the polarization azimuth angle of the beam 1 to be measured

The changes are shown in Table 2. It can be seen from Table 2 that when the direction of the transmission axis of the polarizing prism is parallel to the polarization direction of the beam 1 to be measured

or vertically ( or -90°), the error of the degree of polarization V is 0.

对于偏振度为1的线偏振光，当四分之一波片的相位延迟量δ存在2°误差时，偏振度V的误差ΔV随偏振棱镜的透光轴角度α和待测光束1的偏振方位角

的变化如表3所示。由表3可知，当偏振棱镜的透光轴方向与待测光束1的偏振方向垂直(

或-90°)时，偏振度V的误差为0。For linearly polarized light with a polarization degree of 1, when there is a 2° error in the phase retardation δ of the quarter-wave plate, the error ΔV of the polarization degree V varies with the transmission axis angle α of the polarizing prism and the polarization of the beam 1 to be measured Azimuth

The changes are shown in Table 3. As can be seen from Table 3, when the direction of the transmission axis of the polarizing prism is perpendicular to the polarization direction of the light beam 1 to be measured (

or -90°), the error of the degree of polarization V is 0.

对于偏振度为1的线偏振光，如果偏振棱镜消光比存在误差p＝10000，偏振度V的误差不随偏振棱镜的透光轴的角度变化，为定值-0.0002，可以忽略。For linearly polarized light with a polarization degree of 1, if there is an error p=10000 in the extinction ratio of the polarization prism, the error of the polarization degree V does not change with the angle of the transmission axis of the polarization prism, which is a fixed value -0.0002 and can be ignored.

图2所示为在先技术1提出的投影曝光装置中照明光瞳偏振参数检测装置的示意图。对于投影曝光装置中使用的线偏振光，当相位延迟器件2的快轴角度存在误差时，选择检偏器3的透光轴方向与待测光束1的偏振方向平行或垂直(或接近平行或接近垂直)时，则偏振度V的误差为0(或接近0)；当检偏器3透光轴角度存在误差时，选择检偏器3的透光轴方向与待测光束1的偏振方向平行或垂直(或接近平行或接近垂直)时，偏振度V的误差为0(或接近0)；当相位延迟器件2的相位延迟量存在误差时，选择检偏器3的透光轴方向与待测光束1的偏振方向垂直(或接近垂直)时，偏振度V的误差接近0；当检偏器3的消光比存在误差p＝10000时，检偏器3的透光轴方向的选择不影响偏振度V的结果，且偏振度V的误差很小，可以忽略。FIG. 2 is a schematic diagram of an illumination pupil polarization parameter detection device in the projection exposure device proposed in the prior art 1. FIG. For the linearly polarized light used in the projection exposure device, when there is an error in the fast axis angle of the phase retardation device 2, the direction of the transmission axis of the polarizer 3 is selected to be parallel or perpendicular to the polarization direction of the light beam 1 to be measured (or close to parallel or close to vertical), then the error of the degree of polarization V is 0 (or close to 0); when there is an error in the angle of the transmission axis of the analyzer 3, select the direction of the transmission axis of the analyzer 3 and the polarization direction of the beam 1 to be measured When parallel or vertical (or close to parallel or close to vertical), the error of the degree of polarization V is 0 (or close to 0); when there is an error in the phase delay of the phase delay device 2, the direction of the transmission axis of the polarizer 3 is selected to be the same as When the polarization direction of the light beam 1 to be measured is vertical (or close to vertical), the error of the degree of polarization V is close to 0; when there is an error p=10000 in the extinction ratio of the analyzer 3, the selection of the transmission axis direction of the analyzer 3 is not correct. Affects the result of the degree of polarization V, and the error of the degree of polarization V is very small and can be ignored.

由以上结果可知，当相位延迟器件2和检偏器3存在不同类型误差时，按照投影曝光装置设定的照明光瞳内线偏振光的偏振方向，选择检偏器3透光轴方向与设定的偏振方向平行或垂直(或接近平行或接近垂直)，此时偏振度V的误差等于或接近0，可以有效减小器件的相关误差对光束偏振测量结果的影响。当待测光束1偏振方向未知时，可以在检偏器3透光轴方向任意设定的情况下，预先粗略测量光束的偏振方向，再根据测量结果调整检偏器3透光轴的角度与预先测量的偏振方向平行或垂直，则偏振度V的误差接近0，也可以有效减小器件误差对测量结果的影响。From the above results, it can be seen that when there are different types of errors in the phase retardation device 2 and the analyzer 3, the direction of the transmission axis of the analyzer 3 and the setting of the polarization direction of the linearly polarized light in the illumination pupil set by the projection exposure device The polarization direction is parallel or vertical (or close to parallel or close to vertical), at this time, the error of the degree of polarization V is equal to or close to 0, which can effectively reduce the influence of device-related errors on the beam polarization measurement results. When the polarization direction of the light beam 1 to be measured is unknown, the polarization direction of the light beam can be roughly measured in advance under the condition that the direction of the light transmission axis of the analyzer 3 is set arbitrarily, and then the angle of the light transmission axis of the analyzer 3 and If the pre-measured polarization directions are parallel or perpendicular, the error of the degree of polarization V is close to 0, which can also effectively reduce the influence of device errors on the measurement results.

表1.Δθ＝1°时，ΔV随偏振棱镜3的透光轴角度α和待测光束1的偏振方位角

的变化Table 1. When Δθ=1°, ΔV varies with the transmission axis angle α of the polarizing prism 3 and the polarization azimuth angle of the beam 1 to be measured

The change

表2.Δα＝1°时，ΔV随偏振棱镜3的透光轴角度α和待测光束1的偏振方位角

的变化Table 2. When Δα=1°, ΔV varies with the transmission axis angle α of the polarizing prism 3 and the polarization azimuth angle of the beam 1 to be measured

The change

表3.δ存在2°误差时，ΔV随偏振棱镜3的透光轴角度α和待测光束1的偏振方位角

的变化Table 3. When there is a 2° error in δ, ΔV varies with the transmission axis angle α of the polarizing prism 3 and the polarization azimuth angle of the beam 1 to be measured

The change

Claims

1. method that improves light beam polarization degree measuring accuracy, the device for testing polarization that uses comprises the phase delay device that sets gradually along the apparatus system optical axis, analyzer and photodetector, the output of this photodetector connects signal processing system, but described phase delay device is the rotation of winding apparatus systematic optical axis under the driving of driver, parallel beam to be measured is incident to described phase delay device and analyzer in systematic optical axis, and by described photodetector detection, the electric signal of this photodetector output is sent into described signal processing system and is carried out data processing, it is characterized in that, polarization direction according to described light beam to be measured, adjust the light transmission shaft direction of described analyzer parallel with the polarization direction of described light beam to be measured or vertical after, carry out the measurement of light beam polarization degree to be measured again.

2. the method for raising light beam polarization degree measuring accuracy according to claim 1 is characterized in that: when generally knowing the polarization direction of light beam to be measured, its concrete measuring process is as follows:

1. the light transmission shaft direction of adjusting described analyzer is parallel or vertical with the polarization direction of described light beam to be measured;

2. utilize described device for testing polarization to treat that photometry Shu Jinhang measures and after data processing, finally obtain the Stokes' parameter and the degree of polarization of described light beam to be measured.

3. the method for raising light beam polarization degree measuring accuracy according to claim 1 is characterized in that: when the polarization direction of the unknown light beam to be measured, its concrete measuring process is as follows:

1. utilize described device for testing polarization to measure and after data processing, obtain the Stokes' parameter and the polarization direction of the light beam to be measured first time of light beam to be measured by existing method;

2. the light transmission shaft direction of adjusting described analyzer is parallel or vertical with the polarization direction of described light beam to be measured;

3. utilize described device for testing polarization to treat that photometry Shu Jinhang measures for the second time and after data processing, finally obtain the Stokes' parameter and the degree of polarization of described light beam to be measured.

4. the method for raising light beam polarization degree measuring accuracy according to claim 1 is characterized in that described phase delay device is for producing quarter-wave plate, electrooptic modulator or the light ball modulator of 90 ° of phase delays.

5. the method for raising light beam polarization degree measuring accuracy according to claim 1, it is characterized in that the described phase delay device system for winding of described driver drives optical axis at the uniform velocity rotates, perhaps by driving the position of at least four different angles between fast axle that the phase delay device rotation can be provided with phase delay device and the described analyzer light transmission shaft.

6. the method for raising light beam polarization degree measuring accuracy according to claim 1 is characterized in that described photodetector is two-dimensional array detector or point probe.