A method for measuring the degree of polarization and angular deviation of a polarizer

Abstract

The application provides a method for measuring the polarization degree and angle deviation of a polarizer, which is based on a straight-through light path. After Fourier coefficients a2, b2, a4 and b4 are calculated according to collected light intensity, the polarization degree of the polarizer, the angle deviation between a polarizer and an analyzer, and the polarization performance of a light intensity measuring device can be directly obtained by performing an iterative calculation process. Meanwhile, since the polarization performance of the light intensity measuring device can be directly calculated without additional measurement, sample information introduced in a traditional ellipsometer correction scheme can be excluded.

Description

Technical Field

[0001] This application relates to the field of optical measurement, and more particularly to a method for measuring the degree of polarization and angular deviation of a polarizer. Background Technology

[0002] The manufacturing process of semiconductor very large-scale integrated circuits involves various types of thin film deposition and etching, all of which require high-precision measurement of various information such as thickness, optical constants, and critical dimensions. Non-contact, high-efficiency polarization optics methods are generally employed.

[0003] In polarization optics measurement methods, the optical components that generate and verify the polarization properties of light are called polarizers. A polarizer used to generate polarized light is usually called a polarizer generator, and a polarizer used to verify polarization is called a polarizer analyzer. If light of a specific wavelength band is used as the light source, the device for recording the light intensity is generally a spectrometer.

[0004] A polarizer, or polarizer plate, is an optical device that converts light into linearly polarized light. For example, in an ellipsometer, a polarizer can be used to convert natural light from a light source into linearly polarized light. Ideally, only polarized light in the transmission direction of the polarizer can pass through; the transmittance in that direction is defined as T. Pt When polarized light perpendicular to the projection direction disappears completely, the transmittance in that direction is defined as T. Pe However, due to imperfections in the polarizer, some polarized light perpendicular to the projection direction will still remain, meaning there is a non-zero extinction ratio ∈ p =T Pe / T Pt For accurate calculations, the extinction ratio of the polarizer used in the measurement band needs to be known. In existing technologies, the polarization degree of the polarizer is typically defined as p = (1 - ∈ p ) / (1+∈ p ). Summary of the Invention

[0005] The purpose of this application is to provide a method for measuring the polarization degree and angular deviation of a polarizer.

[0006] According to one aspect of this application, a method for measuring the polarization degree and angular deviation of a polarizer is provided, wherein the method includes:

[0007] The light intensity is measured using a direct optical path, wherein the direct optical path includes a light source, a polarizer, a polarizer, and a light intensity measuring device. The light emitted by the light source is converted into polarized light by the polarizer, and the polarized light is irradiated onto the light intensity measuring device by the polarizer.

[0008] Based on the light intensity, the Fourier coefficients a2, b2, a4, and b4 are calculated, and m is initialized.D12 m D13 Then repeat the following calculation operations until the results converge: calculate p and a based on the following formulas (1) and (2), and calculate m based on P and the following formulas (3) and (4). D12 and m D13 Then, P is calculated based on formulas (1) and (2);

[0009]

[0010]

[0011]

[0012]

[0013] Where, m D12 and m D13 Let P be the polarization response of the light intensity measuring device, P be the angular deviation between the polarizer and the polarimeter (sometimes referred to as P0 in this text), and p be the degree of polarization of the polarizer. 2 +a 2 =1.

[0014] Optionally, the initialization m D12 m D13 P, including: m D12 m D13 P is initialized to 0, 0, and 1 respectively.

[0015] Optionally, the measurement using a direct optical path to collect the measured light intensity includes: using a direct optical path for measurement, controlling the motor to rotate at different angles during the measurement process, and using the light intensity measurement device to record the light intensity at each angle.

[0016] Optionally, the measurement using a direct optical path to collect the measured light intensity includes: using a direct optical path for measurement, controlling the motor to rotate continuously during the measurement process, and continuously collecting the light intensity using the light intensity measuring device.

[0017] Optionally, the light intensity measuring device is a spectrometer or a photodetector.

[0018] Compared with the prior art, this application has the following advantages: Based on a direct optical path, this application provides a scheme that can efficiently measure the polarization degree of a polarizer and the angular deviation between the polarizer and the polarimeter. After calculating the Fourier coefficients a2, b2, a4, and b4 based on the collected light intensity, this scheme can directly obtain the polarization degree of the polarizer, the angular deviation between the polarizer and the polarimeter, and the polarization performance of the light intensity measuring device in a single measurement by performing an iterative calculation process. At the same time, since this application can directly calculate the polarization performance of the light intensity measuring device without adding additional measurements, it can eliminate the sample information introduced when using the traditional ellipsometer correction scheme. Attached Figure Description

[0019] Figure 1 A schematic diagram of a through optical path, as shown in this application, is illustrated.

[0020] Figure 2 An example m of this application is shown. D12 A schematic diagram of the iterative calculation results;

[0021] Figure 3 An example m of this application is shown. D13 A schematic diagram of the iterative calculation results;

[0022] Figure 4 A schematic diagram showing the iterative calculation results of the P0 angle in an example of this application is illustrated.

[0023] Figure 5 A schematic diagram showing the iterative calculation results of the polarization degree p in an example of this application is shown.

[0024] The same or similar reference numerals in the accompanying drawings represent the same or similar parts. Detailed Implementation

[0025] The present invention will now be described in more detail with reference to the accompanying drawings, which illustrate preferred embodiments of the invention. It should be understood that those skilled in the art can modify the invention described herein while still achieving its advantageous effects. Therefore, the following description should be understood as being of general knowledge to those skilled in the art and is not intended to limit the invention.

[0026] The specific structural and functional details disclosed herein are merely representative and are intended to describe exemplary embodiments of this application. However, this application may be implemented in many alternative forms and should not be construed as being limited solely to the embodiments set forth herein.

[0027] It should be understood that although the terms "first," "second," etc., may be used herein to describe various units, these units should not be limited by these terms. These terms are used merely to distinguish one unit from another. For example, without departing from the scope of the exemplary embodiments, a first unit may be referred to as a second unit, and similarly, a second unit may be referred to as a first unit. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0028] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments. Unless the context clearly indicates otherwise, the singular forms “a” and “an” as used herein are also intended to include the plural. It should also be understood that the terms “comprising” and / or “including” as used herein specify the presence of the stated features, integers, steps, operations, units, and / or components, without excluding the presence or addition of one or more other features, integers, steps, operations, units, components, and / or combinations thereof.

[0029] In existing technologies, the polarization degree p of a polarizer is typically defined as (1-∈ p ) / (1+∈ p ), where ∈ P This is the extinction ratio of the polarizer. Ideally, only polarized light in the transmission direction of the polarizer can pass through; the transmittance in that direction is defined as T. Pt When polarized light perpendicular to the transmission direction disappears completely, the transmittance in that direction is defined as T. Pe Extinction ratio ∈ p =T Pe / T Pt However, the accuracy of this method is affected by the polarization properties of the detector and the accuracy of the motor of the rotating polarizer. Based on a through-optical device, this application designs a method that can efficiently measure the polarization degree of a polarizer and the angular deviation between the polarizer and the polarizer. This method can directly obtain the polarization degree of the polarizer, the angular deviation between the polarizer and the polarizer, and the polarization performance of the light intensity measurement device in a single measurement.

[0030] The present application will now be described in further detail with reference to the accompanying drawings.

[0031] This application proposes a method for measuring the polarization degree and angular deviation of a polarizer, wherein the method includes steps S1 and S2. In step S1, a direct optical path is used for measurement to acquire the measured light intensity. The direct optical path includes a light source, a polarizer, a polarizer detector, and a light intensity measuring device. The light emitted by the light source is converted into polarized light by the polarizer, and the polarized light is then irradiated by the polarizer onto the light intensity measuring device. In step S2, Fourier coefficients a2, b2, a4, and b4 are calculated based on the light intensity, and m is initialized. D12 m D13 Then repeat the following calculation operations until the results converge: calculate p and a based on the following formulas (1) and (2), and calculate m based on P and the following formulas (3) and (4). D12 and m D13 Then, P is calculated based on formulas (1) and (2);

[0032]

[0033]

[0034]

[0035]

[0036] Where, m D12 and m D13 Let P be the polarization response of the light intensity measuring device, P be the angular deviation between the polarizer and the polarimeter, and p be the degree of polarization of the polarizer. 2 +a 2 =1. It should be noted that multiple light intensity values ​​can be collected in step S1. For each light intensity value collected by the light intensity measurement device, step S2 can be executed to obtain its corresponding iterative calculation result (i.e., m). D12 m D13 (Iterative calculation results of p, P).

[0037] In some embodiments, the light intensity measuring device is a spectrometer or a photodetector. In some embodiments, the direct optical path also includes essential components for fine-tuning the light beam, such as reflection, focusing, and collimation. Figure 1A schematic diagram of an example direct optical path of this application is shown. This direct optical path includes a light source 101, a polarizer 102, a polarizer 103, and a light intensity measuring device 104. The light intensity measuring device 104 is a spectrometer or a photodetector. Light emitted from the light source 101 is converted into polarized light by the polarizer 102, and this polarized light is then irradiated by the polarizer 103 onto the light intensity measuring device 104. In some embodiments, the light intensity measuring device uses a discrete mode to acquire light intensity. The measurement using the direct optical path includes: using the direct optical path for measurement, controlling the motor to rotate angle successively during the measurement process, and recording the light intensity at each angle using the light intensity measuring device. In some embodiments, the light intensity measuring device uses an integral acquisition mode to acquire light intensity. The measurement using the direct optical path includes: using the direct optical path for measurement, controlling the motor to rotate continuously during the measurement process, and continuously acquiring the light intensity using the light intensity measuring device; in this mode, the light intensity is the total energy of the motor rotating through a certain angle range.

[0038] The polarizer and the polarizer have the same degree of polarization, that is, p is the degree of polarization of the polarizer and also the degree of polarization of the polarizer. For example, the polarizer and the polarizer are polarizers produced in the same batch and have the same product parameters, so they also have the same degree of polarization.

[0039] In this application, considering that the polarization degree of the polarizer and the polarizer may not be strictly equal to 1, the Mueller matrix of the polarizer is expressed as follows:

[0040]

[0041]

[0042] Among them, M p M represents the Mueller matrix of the polarizer. a The Mueller matrix of the polarizer is represented by p, and p represents the polarization degree of the polarizer / polarizer. 2 +a 2 =1. The Mueller matrix M of the light intensity measurement device. d It can be represented as follows:

[0043]

[0044] M d Each item in the table represents the response of the light intensity measurement device to polarization. Based on the aforementioned direct optical path, the light intensity I0 read by the light intensity measurement device is expressed as follows:

[0045]

[0046] Where P represents the angle of the polarizer, A represents the angle of the polarizer, and mD12 and m D13 The light intensity measurement device responds to polarization (see the representation of the Mueller matrix of the light intensity measurement device above). It can be seen that the light intensity I0 read by the detector is related to the angles P and A, and is affected by the polarization performance of the polarizer and the detector performance. It should be noted that in this application, the angle A of the polarizer is set to 0, then P is the angular deviation between the polarizer and the polarizer.

[0047] During the measurement process, the polarizer in the direct optical path remains stationary, while the polarizer rotates at a certain frequency. Therefore, under ideal conditions, the light intensity I obtained by the light intensity measuring device (such as a spectrometer) is as follows:

[0048]

[0049] in, ω is the constant term for light intensity, n is a natural number starting from 1, ω is the angular velocity of the motor, and t is the measurement time. Therefore, the light intensity recorded by the light intensity measuring device can be considered as a Fourier polynomial expanded by the angular velocity of the polarizer motor. Rotating angle A in the above formula I 0, we can obtain the expressions for the four Fourier coefficients a2, b2, a4, and b4, which are formulas (1), (2), (3), and (4) above. At each measurement wavelength, the four Fourier coefficients a2, b2, a4, and b4 can be calculated by measuring the light intensity. Based on formulas (1), (2), (3), and (4) above, it can be seen that there are five unknowns corresponding to each wavelength: P, p, a, and m. D12 ,m D13 Therefore, this application adds a functional relationship between p and a during the iterative calculation process. 2 +a 2 =1.

[0050] In step S2, after calculating the Fourier coefficients a2, b2, a4, and b4 based on the collected light intensity, the iterative calculation process is performed. Specifically, mD12, mD13, and P are initialized first, and then the following calculation operations are repeated until the results converge: p and a are calculated based on the following formulas (1) and (2), and m is calculated based on P and the following formulas (3) and (4). D12 and m D13 P is calculated based on formulas (1) and (2). After iteration, the response of the light intensity measurement device to polarization (i.e., m) can be directly extracted. D12 and m D13 The distribution of polarization degree p of the polarizer within the measurement wavelength range, the distribution of polarization degree p of the polarizer within the measurement wavelength range, and the angle P between the polarizer and the polarizer are all obtained. Thus, it can be seen that the scheme of this application can directly obtain the following three results in one measurement: the polarization degree p of the polarizer, the angular deviation P between the polarizer and the polarizer, and the polarization performance of the light intensity measurement device.

[0051] In some embodiments, the initialization m D12 m D13 P, including: m D12 m D13 P and P are initialized to 0, 0, and 1 respectively. It should be noted that m... D12 m D13 P may also be initialized to other values, which can be set based on empirical values ​​or in combination with actual needs.

[0052] As an example, after obtaining four Fourier coefficients a2, b2, a4, and b4 by measuring light intensity, the following iterative calculation process is performed: 1) Initialization, setting m... D12 m D13 1) Initialize P to 0, 0, and 1 respectively; 2) Calculate p and a from a2 and b2; 3) Calculate m from a4, b4, and P. D12 m D13 ; 4) Calculate P from a2 and b2; 5) Repeat steps 2), 3), and 4) several times until the result converges to obtain m. D12 m D13 The iterative calculation results of P and p. Figure 2 An example m of this application is shown. D12 A schematic diagram of the iterative calculation results; Figure 3 An example m of this application is shown. D13 A schematic diagram of the iterative calculation results; Figure 4 This diagram illustrates the iterative calculation results of the P0 angle (P0angle, i.e., the angle P value between the polarizer and the polarizer) as an example of this application. Figure 5 A schematic diagram showing the iterative calculation results of the polarization degree p in an example of this application is shown.

[0053] Based on a direct optical path, this application presents a scheme for efficiently measuring the polarization degree of a polarizer and the angular deviation between the polarizer and the polarimeter. After calculating the Fourier coefficients a2, b2, a4, and b4 from the collected light intensity, this scheme can directly obtain the polarization degree of the polarizer, the angular deviation between the polarizer and the polarimeter, and the polarization performance of the light intensity measuring device in a single measurement by performing an iterative calculation process. At the same time, since this application can directly calculate the polarization performance of the light intensity measuring device without adding additional measurements, it can eliminate the sample information introduced when using the traditional ellipsometer correction scheme.

[0054] It will be apparent to those skilled in the art that this application is not limited to the details of the exemplary embodiments described above, and that it can be implemented in other specific forms without departing from the spirit or essential characteristics of this application. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of this application is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be embraced within this application. No reference numerals in the claims should be construed as limiting the scope of the claims. Furthermore, it is clear that the word "comprising" does not exclude other units or steps, and the singular does not exclude the plural. Multiple units or devices recited in the system claims may also be implemented by a single unit or device in software or hardware. The terms "first," "second," etc., are used to indicate names and do not indicate any particular order.

Claims

1. A method for measuring the degree of polarization and angular deviation of a polarizer, wherein, The method includes: The light intensity is measured using a direct optical path, which includes a light source, a polarizer, a polarizer, and a light intensity measuring device. The light emitted by the light source is converted into polarized light by the polarizer, and the polarized light is irradiated by the polarizer onto the light intensity measuring device. The polarizer and the polarizer have the same degree of polarization. Based on the light intensity, the Fourier coefficients a2, b2, a4, and b4 are calculated, and m is initialized. D12 m D13 Then repeat the following calculation operations until the results converge: calculate p and a based on the following formulas (1) and (2), and calculate m based on P and the following formulas (3) and (4). D12 and m D13 Then P is calculated based on formulas (1) and (2); （1） （2） （3） （4） Where, m D12 and m D13 Let P be the polarization response of the light intensity measuring device, P be the angular deviation between the polarizer and the polarimeter, and p be the degree of polarization of the polarizer. 2 +a 2 =1.

2. The method according to claim 1, wherein, The initialization m D12 m D13 P, including: m D12 m D13 P is initialized to 0, 0, and 1 respectively.

3. The method according to claim 1, wherein, The measurement using a direct optical path, and the acquisition of the measured light intensity, includes: Measurements are performed using a direct optical path. During the measurement process, the motor is controlled to rotate at different angles, and the light intensity at each angle is recorded using the light intensity measurement device.

4. The method according to claim 1, wherein, The measurement using a direct optical path, and the acquisition of the measured light intensity, includes: Measurements are performed using a direct optical path, and the motor is controlled to rotate continuously during the measurement process. The light intensity is continuously collected using the light intensity measurement device.

5. The method according to any one of claims 1 to 4, wherein, The light intensity measurement device is a spectrometer or a photodetector.

Images