A method for measuring stress in a micro-spot lens

Abstract

This invention provides a method for measuring the stress of micro-spot lenses, comprising: acquiring two left-arm micro-spot lenses and two right-arm micro-spot lenses respectively, and combining them to obtain three sets of micro-spot lens groups, each set including one left-arm micro-spot lens and one right-arm micro-spot lens; sequentially installing each set of micro-spot lens groups on a direct-through dual-rotation Mueller matrix ellipsometer, and obtaining the maximum and minimum phase retardation values ​​by rotating the right-arm micro-spot lens in each set; and calculating the phase retardation of each of the two left-arm and two right-arm micro-spot lenses based on the maximum and minimum phase retardation values ​​obtained from the three sets of micro-spot lens groups. This invention can measure the stress of a lens using a direct-through dual-rotation Mueller matrix ellipsometer, find the maximum and minimum values ​​of the measured stress by rotating the right-arm lens of the ellipsometer, and analytically calculate the stress value of a single lens.

Description

Technical Field

[0001] This invention relates to the field of ellipsometer system calibration, and more specifically, to a method for measuring the stress of a micro-spot lens. Background Technology

[0002] In the semiconductor industry, the measurement of the optical critical dimension (OCD) and the measurement of film thickness in fine structures are directly related to the accuracy and yield of production samples. Ellipsometry, due to its advantages of being non-contact, non-destructive, low-cost, fast, and high-precision, is widely used in advanced semiconductor process monitoring. In ellipsometric measurement, to achieve accurate film thickness measurement, the spot size needs to be minimized. One way to achieve this is to add a micro-spot lens to the front of each of the left and right arms of the ellipsometer to reduce the spot size. Taking a Mueller matrix ellipsometer with a dual-rotation compensator as an example... Figure 1 As shown, its basic configuration includes: a light source 1, a polarizer 2, a first rotary motor 3, a first compensator 4, a left-arm micro-spot lens 5, a right-arm micro-spot lens 6, a second compensator 7, a second rotary motor 8, an analyzer 9, and a spectrometer 10. Micro-spot lenses are typically achromatic lenses composed of several pieces of optical glass. Imperfections in the production and processing of optical glass can lead to residual stress. This stress can cause birefringence of polarized light, altering its polarization state. If the stress in the lens is not controlled, it will ultimately have a significant impact on parameters such as the film thickness and optical constants of the sample under test. Summary of the Invention

[0003] This invention addresses the technical problems existing in the prior art by providing a method for measuring the stress of a micro-spot lens, comprising:

[0004] Two left-arm micro-spot lenses and two right-arm micro-spot lenses are obtained respectively, and three sets of micro-spot lens groups are obtained by combining them. Each set of micro-spot lens groups includes one left-arm micro-spot lens and one right-arm micro-spot lens.

[0005] Each group of micro-spot lenses was installed sequentially on the through-type double-rotation Mueller matrix ellipsometer. The maximum and minimum values ​​of phase delay were obtained by rotating the right-arm micro-spot lens in each group of micro-spot lenses. The left-arm micro-spot lens was installed at the front end of the left arm of the through-type double-rotation Mueller matrix ellipsometer, and the right-arm micro-spot lens was installed at the front end of the right arm of the through-type double-rotation Mueller matrix ellipsometer.

[0006] Based on the maximum and minimum phase delay values ​​obtained from the three sets of micro-spot lens groups, the phase delay of each of the two left-arm micro-spot lenses and the two right-arm micro-spot lenses is calculated. The phase delay of each micro-spot lens characterizes the stress of the micro-spot lens.

[0007] This invention provides a method for measuring the stress of micro-spot lenses. Three sets of micro-spot lens groups are obtained by combining two left-arm micro-spot lenses and two right-arm micro-spot lenses. Each set includes one left-arm micro-spot lens and one right-arm micro-spot lens. Each set is sequentially installed on a direct-access dual-rotation Mueller matrix ellipsometer. By rotating the right-arm micro-spot lens in each set, the maximum and minimum phase retardation values ​​are obtained. Based on the maximum and minimum phase retardation values ​​obtained from the three sets of micro-spot lens groups, the phase retardation of each of the two left-arm and two right-arm micro-spot lenses is calculated. The phase retardation of each micro-spot lens characterizes its stress, and the ellipsometric system can be calibrated based on the stress of each micro-spot lens. This invention can measure the stress of a lens using a direct-access dual-rotation Mueller matrix ellipsometer, find the maximum and minimum stress values ​​by rotating the right-arm lens of the ellipsometer, and analytically calculate the stress value of a single lens. Attached Figure Description

[0008] Figure 1 A schematic diagram of a straight-through double-rotation compensator type Mueller matrix ellipsomer;

[0009] Figure 2 A flowchart of a micro-spot lens stress measurement method provided by the present invention. Detailed Implementation

[0010] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined with each other to form feasible technical solutions. Such combinations are not constrained by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0011] Micro-spot lenses are typically achromatic lenses composed of several pieces of optical glass. During the production and processing of optical glass, residual stress inevitably remains. This stress in the lens causes birefringence of polarized light, altering its polarization state and ultimately affecting the measurement results of the sample. Therefore, a method for quantitatively measuring the stress in micro-spot lenses is needed.

[0012] Figure 2 The flowchart of a micro-spot lens stress measurement method provided by this invention mainly involves measuring the lens stress using a direct-through dual-rotation Mueller matrix ellipsometer, and then obtaining the specific numerical value of the lens stress through formula analysis. Figure 2 As shown, the method includes:

[0013] Step 1: Obtain two left-arm micro-spot lenses and two right-arm micro-spot lenses respectively, and combine them to obtain three sets of micro-spot lens groups. Each set of micro-spot lens groups includes one left-arm micro-spot lens and one right-arm micro-spot lens.

[0014] As an example, two left-arm micro-spot lenses and two right-arm micro-spot lenses were obtained respectively, and three sets of micro-spot lens groups were obtained by combining them, including:

[0015] Two small spot lenses, L1 and L3, on the left arm and two small spot lenses, L2 and L4, on the right arm were acquired respectively.

[0016] The left arm micro-spot lens L1 and the right arm micro-spot lens L2 are combined to form micro-spot lens group A. The left arm micro-spot lens L3 and the right arm micro-spot lens L4 are combined to form micro-spot lens group B. The left arm micro-spot lens L1 and the right arm micro-spot lens L4 are combined to form micro-spot lens group C.

[0017] Step 2: Install each group of micro-spot lenses sequentially on the through-type dual-rotation Mueller matrix ellipsometer, and obtain the maximum and minimum phase delay values ​​by rotating the right-arm micro-spot lens in each group of micro-spot lenses. Specifically, install the left-arm micro-spot lens at the front end of the left arm of the through-type dual-rotation Mueller matrix ellipsometer, and install the right-arm micro-spot lens at the front end of the right arm of the through-type dual-rotation Mueller matrix ellipsometer.

[0018] Understandably, a micro-spot lens group A is installed on the through-type double-rotation Mueller matrix ellipsometer, wherein a left-arm micro-spot lens L1 is installed at the front end of the left arm of the through-type double-rotation Mueller matrix ellipsometer, and a right-arm micro-spot lens L2 is installed at the front end of the right arm of the through-type double-rotation Mueller matrix ellipsometer.

[0019] Among them, the direct-through double-rotation Mueller matrix ellipsometer is a transmission-type measuring device. When no sample is placed in the center of the ellipsometer, the instrument measures the Mueller matrix of air. The Mueller matrix of air is a 4×4 identity matrix, that is, the main diagonal element is m. 11 m 22 m 33 m 44The value is 1 for all other elements and 0 for the rest. The Mueller matrix measured after installing the micro-spot lens shows a significant deviation from the identity matrix. This is because the stress of the micro-spot lens in both arms causes a non-negligible phase delay in the polarized light, resulting in a change in m... 23 m 24 m 42 m 43 The values ​​of these four Mueller elements deviate significantly from 0. The superposition of the phase delays of the two micro-spot lenses in the left and right arms can be calculated using the Mueller matrix. The phase delay is greatest when the fast axis directions of the left and right arm lenses are parallel. The phase delay is the difference between the phase delays of the two lenses when the fast axis directions of the left and right arm lenses are perpendicular. The phase delay of each micro-spot lens can characterize its stress magnitude.

[0020] The air is directly measured using a direct-through Mueller matrix. The phase delay is calculated using the obtained Mueller matrix. The right arm micro-spot lens L2 is continuously rotated until the measured phase delay is at its maximum, and the data is recorded.

[0021] The Mueller matrix M measured after installing a micro-spot lens group A on a direct-access dual-rotation Mueller matrix ellipsometer. meas1 M is the product of the Mueller matrices of the left-arm micro-spot lens L1, the air, and the right-arm micro-spot lens L2. meas1 =M L2 *M air *M L1 The Mueller matrix of air is the identity matrix, so further we have M meas1 =M L2 *M L1 .

[0022] The phase delay is calculated using the obtained Mueller matrix. The physical model of the micro-spot lens group is similar to that of the composite waveplate and can be represented as M. L2 *M L1 = R(ρ)R(-θ)M(δ)R(θ), where ρ represents the optical rotation angle, θ represents the optical axis azimuth angle, δ represents the phase retardation, and R represents the coordinate rotation matrix, where:

[0023]

[0024]

[0025] δ is obtained by fitting the data using regression, i.e., (δ opt θ opt , ρ opt )=argmin||M meas1-R(ρ)R(-θ)M(δ)R(θ)||2, where the subscript "opt" indicates the optimal solution, and ||.||2 represents the L2 norm of the vector. The Mueller matrix is ​​expanded into a vector form by columns before the operation is performed. The resulting δ opt This is the magnitude of the superposition of the phase delays of the left and right arm lenses.

[0026] After mounting the micro-spot lens A on the through-type dual-rotation Mueller matrix ellipsometer, continuously rotate the right-arm micro-spot lens L2 until the measured phase delay is at its maximum. The measured phase delay reaches its maximum when the fast axis direction of the right-arm micro-spot lens L2 is parallel to the fast axis direction of the left-arm micro-spot lens L1, denoted as δ. max1 (δ max1 >0), and its relationship with the phase retardation of the left and right arm lenses is δ max1 =δ1+δ2, where δ1 (δ1>0) represents the phase delay of the left arm micro-spot lens L1, and δ2 (δ2>0) represents the phase delay of the right arm micro-spot lens L2.

[0027] Then, rotate the right-arm micro-spot lens L2 by 90° and record the measured phase delay. Specifically, based on the premise that the fast axis direction of the right-arm micro-spot lens L2 is parallel to the fast axis direction of the left-arm micro-spot lens L1, rotate the right-arm micro-spot lens L2 by 90°. This can be done clockwise or counterclockwise. At this point, the fast axis direction of the right-arm micro-spot lens L2 is perpendicular to the fast axis direction of the left-arm micro-spot lens L1, and the absolute value of the measured phase delay is minimized, denoted as δ. min1 (δ min1 >0), and its relationship with the phase retardation of the left and right arm lenses is δ min1 =|δ1-δ2|.

[0028] Then, a micro-spot lens group B is installed on the through-type dual-rotation ellipsometer, wherein a left-arm micro-spot lens L3 is installed at the front end of the left arm of the through-type dual-rotation Mueller matrix ellipsometer, and a right-arm micro-spot lens L4 is installed at the front end of the right arm of the through-type dual-rotation Mueller matrix ellipsometer.

[0029] Similarly, by rotating the right-arm micro-spot lens L4 so that its fast axis is parallel to the fast axis of the left-arm micro-spot lens L3, the recorded phase delay δ max2 (δ max2 >0) represents the sum of the phase retardations of the left arm micro-spot lens L3 and the right arm micro-spot lens L4, δ max2=δ3 + δ4, where δ3 (δ3 > 0) represents the phase retardation of the left-arm micro-spot lens L3, and δ4 (δ4 > 0) represents the phase retardation of the right-arm micro-spot lens L4. Then, rotate the right-arm micro-spot lens L4 by 90°, either clockwise or counterclockwise. At this point, the fast axis of the right-arm micro-spot lens L4 is perpendicular to the fast axis of the left-arm micro-spot lens L3. The recorded phase retardation δ at this point... min2 (δ min2 >0) represents the difference in phase retardation between lens L3 and lens L4, δ min2 =|δ3-δ4|.

[0030] Then, a micro-spot lens group C is installed on the through-type double-rotation ellipsometer. Specifically, a left-arm micro-spot lens L1 is installed at the front end of the left arm of the through-type double-rotation Mueller matrix ellipsometer, and a right-arm micro-spot lens L4 is installed at the front end of the right arm of the through-type double-rotation Mueller matrix ellipsometer.

[0031] Similarly, by rotating the right-arm micro-spot lens L4 so that its fast axis is parallel to the fast axis of the left-arm micro-spot lens L1, the recorded phase delay δ is... max3 (δ max3 >0) represents the sum of the phase retardations of the left arm micro-spot lens L1 and the right arm micro-spot lens L4, δ max3 =δ1 + δ4, where δ1 (δ1 > 0) represents the phase retardation of the left-arm micro-spot lens L1, and δ4 (δ4 > 0) represents the phase retardation of the right-arm micro-spot lens L4. Then, rotate the right-arm micro-spot lens L4 by 90°, either clockwise or counterclockwise. At this point, the fast axis of the right-arm micro-spot lens L4 is perpendicular to the fast axis of the left-arm micro-spot lens L1. The recorded phase retardation δ at this point... min3 (δ min2 >0) represents the difference in phase retardation between lens L3 and lens L4, δ min3 =|δ1-δ4|.

[0032] Step 3: Based on the maximum and minimum phase delay values ​​obtained from the three sets of micro-spot lens groups, calculate the phase delay of each of the two left-arm micro-spot lenses and the two right-arm micro-spot lenses. The phase delay of each micro-spot lens characterizes the stress of the micro-spot lens.

[0033] Understandably, the phase delay of each micro-spot lens L1, L2, L3, and L54 is calculated based on the six phase delay data obtained from the above steps. Six equations are derived from these steps.

[0034] δ max1 =δ1+δ2,

[0035] δ min1 =|δ1-δ2|,

[0036] δ max2 =δ3+δ4,

[0037] δ min2 =|δ3-δ4|,

[0038] δ max3 =δ1+δ4,

[0039] δ min3 =|δ1-δ4|,

[0040] The values ​​of δ1, δ2, δ3, and δ4 can be solved from these 6 equations, which represent the stress magnitude of the corresponding micro-spot lenses. The phase delay of each micro-spot lens characterizes its respective stress magnitude. The ellipsometer system is calibrated based on the stress magnitude of each micro-spot lens.

[0041] This invention provides a method for measuring the stress of micro-spot lenses. Three sets of micro-spot lens groups are obtained by combining two left-arm micro-spot lenses and two right-arm micro-spot lenses. Each set includes one left-arm micro-spot lens and one right-arm micro-spot lens. Each set is sequentially installed on a direct-access dual-rotation Mueller matrix ellipsometer. By rotating the right-arm micro-spot lens in each set, the maximum and minimum phase retardation values ​​are obtained. Based on the maximum and minimum phase retardation values ​​obtained from the three sets of micro-spot lens groups, the phase retardation of each of the two left-arm and two right-arm micro-spot lenses is calculated. The phase retardation of each micro-spot lens characterizes its stress, and the ellipsometric system can be calibrated based on the stress of each micro-spot lens. This invention utilizes a direct-access dual-rotation Mueller matrix ellipsometer to measure the stress of a lens, finds the maximum and minimum stress values ​​by rotating the right-arm lens of the ellipsometer, and analytically calculates the stress value of a single lens.

[0042] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0043] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0044] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for measuring stress in a micro-spot lens, characterized in that, include: Two left-arm micro-spot lenses and two right-arm micro-spot lenses are obtained respectively, and three sets of micro-spot lens groups are obtained by combining them. Each set of micro-spot lens groups includes one left-arm micro-spot lens and one right-arm micro-spot lens. Each group of micro-spot lenses was installed sequentially on the through-type double-rotation Mueller matrix ellipsometer. The maximum and minimum values ​​of phase delay were obtained by rotating the right-arm micro-spot lens in each group of micro-spot lenses. The left-arm micro-spot lens was installed at the front end of the left arm of the through-type double-rotation Mueller matrix ellipsometer, and the right-arm micro-spot lens was installed at the front end of the right arm of the through-type double-rotation Mueller matrix ellipsometer. Based on the maximum and minimum phase delay values ​​obtained from the three sets of micro-spot lens groups, the phase delay of each of the two left-arm micro-spot lenses and the two right-arm micro-spot lenses is calculated. The phase delay of each micro-spot lens characterizes the stress of the micro-spot lens.

2. The method for measuring the stress of a micro-spot lens according to claim 1, characterized in that, Two micro-spot lenses from the left arm and two micro-spot lenses from the right arm were obtained respectively, and three sets of micro-spot lens groups were obtained by combining them, including: Two small spot lenses, L1 and L3, on the left arm and two small spot lenses, L2 and L4, on the right arm were acquired respectively. The left arm micro-spot lens L1 and the right arm micro-spot lens L2 are combined to form micro-spot lens group A. The left arm micro-spot lens L3 and the right arm micro-spot lens L4 are combined to form micro-spot lens group B. The left arm micro-spot lens L1 and the right arm micro-spot lens L4 are combined to form micro-spot lens group C.

3. The method for measuring the stress of a micro-spot lens according to claim 2, characterized in that, The process involves sequentially installing each group of micro-spot lenses on a direct-access dual-rotation Mueller matrix ellipsometer, and obtaining the maximum and minimum phase retardation values ​​by rotating the right-arm micro-spot lens in each group, including: A micro-spot lens group A is installed on a direct-access dual-rotation Mueller matrix ellipsometer. By rotating the right-arm micro-spot lens L2 in the micro-spot lens group A, the fast axis direction of the right-arm micro-spot lens L2 is made parallel to the fast axis direction of the left-arm micro-spot lens L1, and the maximum value of the phase delay δ is obtained. max1 ; Rotate the right arm micro-spot lens by 90° and measure the minimum phase delay δ at this point. min1 ; Micro-spot lens group B was installed sequentially on the through-type double-rotating Mueller matrix ellipsometer, and the maximum value of the phase delay δ was obtained using the same method. max2 and the minimum phase delay δ min2 Furthermore, by installing a micro-spot lens group C on a through-type double-rotating Mueller matrix ellipsometer, the maximum value of the phase delay δ was obtained using the same method. max3 and the minimum phase delay δ min3 .

4. The method for measuring the stress of a micro-spot lens according to claim 3, characterized in that, The maximum phase delay δ is obtained when the fast axis direction of the right arm micro-spot lens L2 is parallel to the fast axis direction of the left arm micro-spot lens L1. max1 The relationship between the phase retardation of the left and right arm micro-spot lenses is: δ max1 =δ1+δ2; The minimum phase delay δ is obtained when the fast axis direction of the right arm micro-spot lens L2 is perpendicular to the fast axis direction of the left arm micro-spot lens L1. min1 The relationship between the phase retardation of the left and right arm micro-spot lenses is: δ min1 =|δ1-δ2|; Where δ1>0 represents the phase delay of the left arm micro-spot lens L1, and δ2>0 represents the phase delay of the right arm micro-spot lens L2.

5. The method for measuring the stress of a micro-spot lens according to claim 4, characterized in that, The maximum phase delay δ is obtained when the fast axis direction of the right arm micro-spot lens L4 is parallel to the fast axis direction of the left arm micro-spot lens L3. max2 The relationship between the phase retardation of the left and right arm micro-spot lenses is: δ max2 =δ3 + δ4; The minimum phase delay δ is obtained when the fast axis direction of the right arm micro-spot lens L4 is perpendicular to the fast axis direction of the left arm micro-spot lens L3. min2 The relationship between the phase retardation of the left and right arm micro-spot lenses is: δ min2 =|δ3-δ4|; Wherein, δ3>0 represents the phase delay of the left arm micro-spot lens L3, and δ4>0 represents the phase delay of the right arm micro-spot lens L4.

6. The method for measuring the stress of a micro-spot lens according to claim 5, characterized in that, The maximum phase delay δ is obtained when the fast axis direction of the right arm micro-spot lens L4 is parallel to the fast axis direction of the left arm micro-spot lens L1. max3 The relationship between the phase retardation of the left and right arm micro-spot lenses is: δ max3 =δ1 + δ4; The minimum phase delay δ is obtained when the fast axis direction of the right arm micro-spot lens L4 is perpendicular to the fast axis direction of the left arm micro-spot lens L1. min3 The relationship between the phase retardation of the left and right arm micro-spot lenses is: δ min3 =|δ1-δ4|; Wherein, δ1>0 represents the phase delay of the left arm micro-spot lens L1, and δ4>0 represents the phase delay of the right arm micro-spot lens L4.

7. The method for measuring the stress of a micro-spot lens according to claim 6, characterized in that, The phase retardation of the two left-arm micro-spot lenses and the two right-arm micro-spot lenses is calculated based on the maximum and minimum phase retardation values ​​obtained from the three sets of micro-spot lens groups, including: Construct the solution equation: d max1 =δ1+δ2, d min1 =|δ1-δ2|, d max2 =δ3+δ4, d min2 =|δ3-δ4|, d max3 =δ1+δ4, d min3 =|δ1-δ4|, Where, δ max1 δ min1 δ max2 δ min2 δ max3 and δ min3 Given the values ​​of δ1, γ2, δ3 and δ4, the phase delay of the left arm micro-spot lens L1, the right arm micro-spot lens L2, the left arm micro-spot lens L3 and the right arm micro-spot lens L4 are obtained by solving the equation.

8. The method for measuring the stress of a micro-spot lens according to claim 1, characterized in that, The obtained phase retardation is calculated based on the measured Mueller matrix, where the Mueller matrix M = R(ρ)R(-θ)M(δ)R(θ), ρ represents the optical rotation angle, θ represents the optical axis azimuth angle, γ represents the phase retardation, and R represents the coordinate rotation matrix. δ is obtained by fitting the data using regression, i.e., (δ) opt ,θ opt ,ρ opt )=argmin‖M meas1 -R(ρ)R(-θ)M(δ)R(θ)‖2, where the subscript "opt" indicates the optimal solution, and ‖.‖2 represents the L2 norm of the vector. The Mueller matrix M is expanded into a vector form by columns before the operation is performed to obtain δ. opt This refers to the magnitude of the superposition of the phase delays of the left and right arm micro-spot lenses.

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