High-precision extraction method for optical parameters of ellipsometer

Abstract

The invention provides an ellipsometer optical parameter high-precision extraction method, solves the technical problems that an existing ellipsometer optical parameter extraction method is low in convergence speed, low in robustness, low in parameter extraction precision and depends on an initial input value, and has the advantages of being high in convergence speed, high in robustness, high in parameter extraction precision, insensitive to the initial input value and the like. The method can be suitable for high-precision measurement of film parameters in the fields of wafer manufacturing, optical coating and the like, and can realize high-precision extraction of optical parameters such as film thickness and refractive index.

Description

Technical Field

[0001] The invention belongs to the technical field of optical precision measurement, and in particular to the technical field of ellipsometer optical parameter measurement, and specifically is a method for high-precision extraction of ellipsometer optical parameters. Background Art

[0002] Unlike scanning electron microscopes, atomic force microscopes, and transmission electron microscopes that directly measure the parameters of samples, ellipsometry is not a "what you see is what you get" technology. In essence, ellipsometry uses the polarization characteristics of light to obtain information about the sample to be measured, and the extraction of thin film optical parameters has always been a difficult point in ellipsometry to obtain high-precision thin film structural parameters.

[0003] Because the ellipsometric equation is a complex transcendental equation, in order to obtain the structural parameters of a general thin film, the ellipsometric parameters need to be subjected to a complex inversion iterative data processing process. Moreover, it is different from the general optical system solution, which can usually be satisfied by optimizing the solution, while the ellipsometric measurement requires a high-precision true solution. Therefore, when the inversion algorithm is improperly selected or the data processing is not perfect, a pseudo-solution will be obtained and it will not be easy to be discovered. Therefore, optical parameter extraction technology has always been the focus of the ellipsometer research field.

[0004] Existing ellipsometry optical parameter extraction methods are generally slow and highly dependent on the selection of initial sample parameter values. The deviation between the initial sample parameter values ​​that need to be input and their true values ​​cannot be too large, otherwise the evaluation function will fall into a local minimum during the iterative calculation process, making it impossible to obtain the correct film parameter values, and the parameter extraction accuracy is low. Summary of the invention

[0005] In order to solve the technical problems of low convergence speed, low robustness, low parameter extraction accuracy and dependence on initial input values ​​in existing ellipsometer optical parameter extraction methods, the present invention provides a high-precision extraction method for ellipsometer optical parameters.

[0006] The technical solution of the present invention is:

[0007] A method for extracting optical parameters of an ellipsometer with high precision comprises the following steps:

[0008] Step 1: Based on the structure model of the sample to be tested, a mathematical function relationship between the sample parameters to be tested and the ellipsometric parameters is established;

[0009] Step 2: give the initial estimated value of the sample parameter to be tested and proceed to step 3;

[0010] Step 3, according to the parameters of the sample to be tested entering this step and the mathematical function relationship between the parameters of the sample to be tested and the ellipsometric parameters, the theoretical ellipsometric parameter values ​​are calculated;

[0011] Step 4, bringing the theoretical ellipsometric parameter values ​​and the sample measured ellipsometric parameter values ​​into the evaluation function, and calculating the evaluation function result;

[0012] Step 5: Determine whether the evaluation function result obtained in step 4 is the global minimum. If it is not the global minimum, use the optimization method to obtain new parameters of the sample to be tested, and return to step 3 for iterative calculation; if it is the global minimum, directly output the corresponding sample parameters.

[0013] Furthermore, in step 1, the sample structure model includes the cross-sectional structural composition of the sample, the optical parameters of the materials of different layers of the sample, and the reflection and transmission of the incident light at the interfaces of different layers of the sample.

[0014] Furthermore, the optical parameters of the different layers of materials in the sample include refractive index n and thickness d.

[0015] Furthermore, the ellipsometric parameters are the phase difference Δ and the azimuth angle ψ. The mathematical function relationship between the sample parameters and the ellipsometric parameters of the thin film sample is as follows:

[0016]

[0017] Among them, n0 is the refractive index of the upper medium of the thin film material; θ0 is the incident angle in the upper medium of the thin film material; n1 is the refractive index of the thin film material; θ1 is the incident angle in the thin film material; n2 is the refractive index of the lower medium of the thin film material; θ2 is the refractive angle in the lower medium of the thin film material; d1 is the thickness of the thin film material; λ is the incident wavelength.

[0018] Furthermore, in step 4, the calculation formula of the evaluation function is:

[0019]

[0020] Where M is the total number of measurements, N c , C c , S c is calculated based on the theoretical value of ellipsometric parameters, N m , C m , S m It is calculated based on the actual measured values ​​of the ellipsometric parameters, and the corresponding calculation formulas are:

[0021]

[0022] Where ψ c and Δ c is the azimuth and phase difference calculated from the sample parameters, ψ m and Δ m are the azimuth and phase difference values ​​measured during the experiment.

[0023] Furthermore, in step 5, a nonlinear regression parameter least squares estimation method is used to obtain new parameters of the sample to be tested.

[0024] Effects of the Invention

[0025] The technical effect of the present invention is that a high-precision extraction method for optical parameters of an ellipsometer provided by the present invention defines an evaluation function and uses the least squares estimation method of regression parameters in nonlinear regression for iterative calculation. It has the advantages of fast convergence speed, high robustness, high parameter extraction accuracy, and independence from initial input values. It can be applied to high-precision measurement of thin film parameters in the fields of wafer manufacturing, optical coating, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a schematic diagram of the structure of an ellipsometer system provided by the present invention.

[0027] Figure 2 A parameter extraction flow chart of a method for high-precision extraction of optical parameters of an ellipsometer provided by the present invention.

[0028] Figure 3 The figure is a schematic diagram comparing the theoretical calculated values ​​and the measured values ​​of a set of ellipsometric parameters provided by the present invention, wherein (a) is a comparison diagram of the phase difference measured and the theoretical calculated values, and (b) is a comparison diagram of the azimuth angle measured and the theoretical calculated values.

[0029] Figure 4 A set of evaluation functions and sample thickness parameter iterative process curve results provided by the present invention, wherein (a) is a 50nm film thickness extraction result diagram, (b) is a 100nm film thickness extraction result diagram, (c) is a 200nm film thickness extraction result diagram, and (d) is a 500nm film thickness extraction result diagram. DETAILED DESCRIPTION

[0030] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the present invention.

[0031] In order to make the purpose, content and advantages of the present invention clearer, the specific implementation of the present invention is further described in detail below in conjunction with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0032] See also Figure 1-Figure 4 The present invention provides a method for extracting optical parameters of an ellipsometer with high precision, comprising the following steps:

[0033] Step 1: Based on the structure model of the sample to be tested, a mathematical function relationship between the parameters of the sample to be tested and the ellipsometric parameters is established; wherein the structure model of the sample to be tested includes the cross-sectional structure composition of the sample, the optical parameters of the materials of different layers of the sample, and the reflection and transmission of the incident light at the interfaces of different layers of the sample; and the cross-sectional structure composition of the sample includes the sample base layer, thin film layers of different thicknesses, and air, and the optical parameters of the materials of different layers of the sample generally include the refractive index n and the thickness d.

[0034] Step 2: give the initial estimated value of the sample parameter to be tested and proceed to step 3;

[0035] Step 3: Calculate the theoretical ellipsometric parameter values ​​according to the parameters of the sample to be tested entering this step and the mathematical function relationship between the parameters of the sample to be tested and the ellipsometric parameters; the parameters of the sample to be tested are the refractive index n and thickness d of the film, and the ellipsometric parameters are the phase difference Δ and the azimuth angle ψ. The mathematical function relationship formula between the sample parameters of the film sample and the ellipsometric parameters is:

[0036]

[0037] Among them, n0 is the refractive index of the upper medium of the thin film material; θ0 is the incident angle in the upper medium of the thin film material; n1 is the refractive index of the thin film material; θ1 is the incident angle in the thin film material; n2 is the refractive index of the lower medium of the thin film material; θ2 is the refractive angle in the lower medium of the thin film material; d1 is the thickness of the thin film material; λ is the incident wavelength.

[0038] Step 4: Substitute the theoretical ellipsometric parameter values ​​and the sample measured ellipsometric parameter values ​​into the evaluation function to calculate the evaluation function result; the calculation formula of the evaluation function is:

[0039]

[0040] Where M is the total number of measurements, N c , C c , S c and N m , C m , S m They are the coordinate units of the three directions in the spherical coordinate system, where N c , C c , Sc Calculated by the theoretical value of ellipsometric parameters, N m , C m , S m It is calculated through the actual measured values ​​of the ellipsometric parameters, and the corresponding calculation formulas are:

[0041]

[0042] Where ψ c and Δ c is the azimuth and phase difference calculated from the sample parameters, ψ m and Δ m are the azimuth and phase difference values ​​measured during the experiment.

[0043] Step 5: determine whether the evaluation function result obtained in step 4 is the global minimum. If it is not the global minimum, an optimization method is used to obtain new parameters of the sample to be tested, and the process returns to step 3 for iterative calculation. In this embodiment, a nonlinear regression parameter least squares estimation method is used to obtain new parameters of the sample to be tested.

[0044] like Figure 1 As shown, it is a schematic diagram of the structure of an ellipsometer system provided in this embodiment. The measured ellipsometric parameters of the sample in the high-precision extraction method of optical parameters of the ellipsometer provided by the present invention can be obtained by the ellipsometer system experiment. The ellipsometer system structure mainly includes a light source, a polarizing arm, an analyzing arm and a detector, wherein the polarizing arm is sequentially composed of a collimating lens, a polarizer, a motor and an achromatic wave plate inside the motor, and the analyzing arm is sequentially composed of a motor, an achromatic wave plate inside the motor, an analyzer and a collimating lens.

[0045] like Figure 2 As shown, it is an extraction flow chart of the high-precision extraction method of optical parameters of an ellipsometer proposed in the present invention, and the specific steps are: based on the structural model of the sample to be tested, combined with the principle of reflection and transmission of polarized light interface, a mathematical function relationship between the sample parameters to be tested and the ellipsometric parameters is established, given an initial estimated value of the sample parameters to be tested, the theoretical ellipsometric parameters are calculated through the mathematical function relationship between the sample parameters and the ellipsometric parameters, the theoretical ellipsometric parameters and the measured ellipsometric parameters are input into the evaluation function, and the evaluation function result is calculated, when the evaluation function result does not meet the global minimum condition, iterative calculation is performed using a nonlinear regression algorithm to find the most suitable sample parameters in the world, and the evaluation function is continued to be calculated based on the sample parameters found, and when the evaluation function result meets the global minimum condition, the corresponding sample parameters are directly output.

[0046] like Figure 3 FIG. 1 is a schematic diagram showing a comparison between a set of theoretical calculated values ​​and measured values ​​of ellipsometric parameters provided in this embodiment, wherein Figure 3(a) is a comparison of the theoretical phase difference (i.e., phase delay) versus wavelength curve calculated from the given initial values ​​of the parameters of the sample to be tested and the actual phase difference versus wavelength curve obtained from experimental measurement. Figure 3 (b) is a comparison of the theoretical azimuth angle versus wavelength curve calculated based on the given initial values ​​of the sample parameters to be tested and the actual azimuth angle versus wavelength curve obtained by experimental measurement. In the process of extracting the optical parameters of the ellipsometer, there will be a large gap between the theoretical ellipsometric parameters calculated based on the given initial values ​​of the sample parameters to be tested and the experimentally measured values. In the process of continuously iterating the sample parameters through the nonlinear regression algorithm, the theoretical ellipsometric parameters and the ellipsometric parameters obtained by experimental measurement will continue to approach each other, thereby finally obtaining a sample parameter value with high accuracy that meets the evaluation function result.

[0047] like Figure 4 As shown in FIG. 1 , a set of evaluation functions and sample thickness parameter iterative change process curve results provided in this embodiment are shown. Figure 4 (a)- Figure 4 (d) are curve results of the iterative changes of the evaluation function with the sample thickness during the thickness parameter extraction process for samples with nominal film thickness of 50nm, 100nm, 200nm and 500nm respectively; the thickness parameters of four samples with different film thicknesses extracted by the parameter extraction method provided by the present invention have an error of no more than 0.5nm with the corresponding nominal thickness value of the sample.

[0048] In summary, the present invention can achieve high-precision extraction of optical parameters such as film thickness and refractive index; compared with other technologies, this method has the advantages of fast convergence speed, high robustness, high parameter extraction accuracy, and insensitivity to initial input values. It can be applied to high-precision measurement of thin film parameters in the fields of wafer manufacturing, optical coating, etc.

[0049] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0050] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A high-precision extraction method for optical parameters of an ellipsometer, characterized in that: The following steps are involved: Step 1: Based on the structure model of the sample to be tested, a mathematical function relationship between the parameters of the sample to be tested and the ellipsometric parameters is established; Step 2: give the initial estimated value of the sample parameter to be tested and proceed to step 3; Step 3, according to the parameters of the sample to be tested entering this step and the mathematical function relationship between the parameters of the sample to be tested and the ellipsometric parameters, the theoretical ellipsometric parameter values ​​are calculated; Step 4, bring the theoretical ellipsometric parameter values ​​and the sample measured ellipsometric parameter values ​​into the evaluation function to calculate the evaluation function result; Step 5: Determine whether the evaluation function result obtained in step 4 is the global minimum. If it is not the global minimum, use the optimization method to obtain new parameters of the sample to be tested, and return to step 3 for iterative calculation; if it is the global minimum, directly output the corresponding sample parameters.

2. A high-precision extraction method for optical parameters of an ellipsometer as claimed in claim 1, characterized in that: In step 1, the sample structure model includes the cross-sectional structure composition of the sample, the optical parameters of the materials of different layers of the sample, and the reflection and transmission parameters of the incident light at the interfaces of different layers of the sample.

3. A high-precision extraction method for optical parameters of an ellipsometer as claimed in claim 2, characterized in that: The optical parameters of the materials of different layers of the sample include refractive index n and thickness d.

4. A method for extracting optical parameters of an ellipsometer with high precision as claimed in claim 1 or 3, characterized in that: The ellipsometric parameters are the phase difference Δ and the azimuth angle ψ. The mathematical function relationship between the sample parameters and the ellipsometric parameters of the thin film sample is as follows: Among them, n0 is the refractive index of the upper medium of the thin film material; θ0 is the incident angle in the upper medium of the thin film material; n1 is the refractive index of the thin film material; θ1 is the incident angle in the thin film material; n2 is the refractive index of the lower medium of the thin film material; θ2 is the refractive angle in the lower medium of the thin film material; d1 is the thickness of the thin film material; λ is the incident wavelength.

5. A high-precision extraction method for optical parameters of an ellipsometer as claimed in claim 1, characterized in that: In step 4, the calculation formula of the evaluation function is: Where M is the total number of measurements, N c , C c , S c is calculated based on the theoretical value of ellipsometric parameters, N m , C m , S m It is calculated based on the actual measured values ​​of the ellipsometric parameters, and the corresponding calculation formulas are: Where ψ c and Δ c is the azimuth and phase difference calculated from the sample parameters, ψ m and Δ m are the azimuth and phase difference values ​​measured during the experiment.

6. A high-precision extraction method for optical parameters of an ellipsometer as claimed in claim 1, characterized in that: In step 5, the nonlinear regression parameter least squares estimation method is used to obtain new parameters of the sample to be tested.

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