CN114593700B - Nano-structure scattered field calculation method for X-ray key size measurement - Google Patents

Abstract

The invention belongs to the field of X-ray key dimension measurement methods, and particularly relates to a nanostructure scattered field calculation method for X-ray key dimension measurement, which comprises the following steps: describing an area surrounded by a curve in an XOZ coordinate system and an X coordinate axis of the XOZ coordinate system as a section outline of a periodic unit of the nano structure, wherein the X coordinate axis represents the periodic arrangement direction of the periodic unit of the nano structure in an entity space, and the Z coordinate axis represents the direction vertical to a substrate plane where the nano structure is positioned; the curve is generated by selecting points in an XOZ coordinate system; and calculating a reciprocal space value of the cross section profile at a specific coordinate position in a reciprocal space through non-uniform fast Fourier transform, and taking the reciprocal space value as a shape factor of the nano structure to calculate a scattering field of the nano structure. The method is suitable for the nano structure with any section surface type, and solves the problems of difficult modeling and poor fitting degree existing in the prior art that the section outline can only be described by simple geometric shape superposition.

Description

A Calculation Method of Nanostructure Scattering Field for X-ray Critical Dimension Measurement

technical field

The invention belongs to the field of measuring methods for X-ray critical dimensions, and more particularly relates to a method for calculating scattered fields of nanostructures used for measuring X-ray critical dimensions.

Background technique

The X-ray critical dimension measurement method is an optical measurement method that uses the distribution information of the scattered field after X-rays are scattered by the sample to obtain the information of the sample to be measured. The basic principle is to irradiate the sample with a beam of collimated X-rays and measure The reciprocal spatial information of the sample is obtained from the scattering signal of the sample in the small angle range, and then the information of the sample to be tested is extracted from it.

In recent years, due to the continuous complexity of nanostructures, traditional small-angle scattering analysis can no longer meet the demand for reconstruction of sample information. Therefore, the X-ray critical dimension measurement method changes the incident angle relative to the incident light by rotating the sample to obtain more comprehensive reciprocal space information. However, when using the X-ray critical dimension measurement method for simulation, since the actually manufactured nanostructures often have very complex shapes, a method that can accurately describe the periodic units of nanostructures and accurately calculate their shape factors is needed.

The current description of the periodic unit of nanostructures is mainly represented by the superposition of multiple basic shapes. The literature (Bernard Croset. Form factor of any polyhedron: a general compact formula and its singularities. J. Appl. Cryst. (2017). 50, 1245-1255) gives the formula for calculating the shape factor of any polyhedron. Taking the grating as an example, the X-ray critical dimension measurement method uses multiple trapezoidal superpositions to approximate the actual grating profile. However, the actual manufactured grating cannot be described by ideal geometric figures, and the existence of roughness makes it more difficult to describe the cross-sectional profile by analytical methods. Therefore, how to accurately describe the cross-sectional profile of the periodic unit of the nanostructure and calculate its scattering field information must be carefully considered and analyzed.

Contents of the invention

Aiming at the defects and improvement needs of the prior art, the present invention provides a method for calculating the scattering field of nanostructures for the measurement of X-ray critical dimensions. Modeling difficulties and poor fitting problems caused by contours.

In order to achieve the above object, according to one aspect of the present invention, a method for calculating the scattered field of nanostructures for X-ray critical dimension measurement is provided, including:

The area enclosed by the curve in the XOZ coordinate system and the X coordinate axis of the XOZ coordinate system is described as the cross-sectional profile of the periodic unit of the nanostructure, wherein the X coordinate axis represents the periodic unit of the nanostructure in the entity The direction of spatial periodic arrangement, the Z coordinate axis of the XOZ coordinate system represents the direction perpendicular to the substrate plane where the nanostructure is located; the curve is generated by selecting points in the XOZ coordinate system;

Calculate the reciprocal space value of the cross-sectional profile at a specific coordinate position in the reciprocal space by non-uniform fast Fourier transform, as the shape factor of the nanostructure;

Using the shape factors, the nanostructure scattering field for X-ray critical dimension measurements is calculated.

Further, the curve is formed by selecting control points in the XOZ coordinate system and adopting a spline method, wherein the selection is randomly selected or selected according to needs.

Further, the curve is determined by selecting the number of terms of the polynomial and the coefficient of each term, wherein the selection is randomly selected or selected according to needs.

Further, the specific coordinate position is obtained as follows:

According to the position of the detector, the pixel size of the detector and the incident angle relative to the sample when the actual X-rays irradiate the sample, the reciprocal space coordinate corresponding to the scattered field signal collected actually is calculated as the specific coordinate position.

The present invention also provides a nanostructure scattering field calculation device for X-ray critical dimension measurement, including:

The cross-sectional profile description module is used to describe the area enclosed by the curve in the XOZ coordinate system and the X coordinate axis in the XOZ coordinate system as the cross-sectional profile of the periodic unit of the nanostructure, wherein the X coordinate axis represents The direction in which the periodic units of the nanostructure are periodically arranged in the physical space, the Z coordinate axis in the XOZ coordinate system represents the direction perpendicular to the substrate plane where the nanostructure is located; the curve passes through the XOZ coordinate system The selected point is calculated and generated;

The calculation module is used to calculate the reciprocal space value of the cross-sectional profile at a specific coordinate position in the reciprocal space through non-uniform fast Fourier transform, as the shape factor of the nanostructure; and using the shape factor to calculate Nanostructured Scattering Fields for X-ray Critical Dimension Measurements.

Further, the curve is formed by selecting control points in the XOZ coordinate system and adopting a spline method, wherein the selection is randomly selected or selected according to needs.

Further, the curve is determined by selecting the number of terms of the polynomial and the coefficient of each term, wherein the selection is randomly selected or selected according to needs.

Further, the specific coordinate position is obtained as follows:

According to the position of the detector, the pixel size of the detector and the incident angle relative to the sample when the actual X-rays irradiate the sample, the reciprocal space coordinate corresponding to the scattered field signal collected actually is calculated as the specific coordinate position.

The present invention also provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the above method for calculating the scattered field of nanostructures for X-ray critical dimension measurement is realized.

The present invention also provides an electronic device, including: a processor, a transceiver, and the above-mentioned computer-readable storage medium, wherein,

The transceiver is used to send and receive data under the control of the processor;

When the processor executes the computer program on the computer-readable storage medium, the steps of the above-mentioned method for calculating the scattered field of nanostructures for X-ray critical dimension measurement are realized.

Generally speaking, through the above technical solutions conceived by the present invention, the following beneficial effects can be obtained:

(1) The present invention proposes a new section outline description method, which establishes a curve in the XOZ coordinate system, and the curve is generated by selecting points in the XOZ coordinate system, and the curve located in the XOZ coordinate system is combined with the X coordinate of the XOZ coordinate system The area enclosed by the axis is described as the cross-sectional profile of the periodic unit of the nanostructure. This method can avoid the existing problems of modeling difficulties and poor fitting caused by the superposition of simple geometric shapes. It can be used for any surface type The nanostructures were described and simulated.

(2) The present invention proposes a method capable of realizing non-uniform sampling, and a method of calculating the light intensity distribution at a given reciprocal space coordinate to improve accuracy.

(3) The present invention adopts polynomial or spline curve to establish the curve used to describe the profile of the section, and the number of sampling points can be flexibly adjusted according to the precision requirement.

In summary, the method of the present invention can be applied to the simulation and optimization requirements of the X-ray critical dimension method for complex nanostructures.

Description of drawings

Fig. 1 is a block diagram of a calculation method for nanostructure scattered field for X-ray critical dimension measurement provided by an embodiment of the present invention;

Fig. 2 is a grating cross-sectional view controlled by a cubic uniform B-spline curve provided by an embodiment of the present invention;

Fig. 3 is the grating scattering field diagram controlled by the cubic uniform B-spline curve provided by the embodiment of the present invention;

Fig. 4 is a schematic diagram of the principle of the X-ray critical dimension method provided by the embodiment of the present invention;

Fig. 5 is a flow chart of the calculation method of the scattering field of any surface nanostructure in the non-uniform fast Fourier transform-based X-ray critical dimension method provided by the embodiment of the present invention;

Fig. 6 is a schematic structural diagram of a nanostructure scattered field calculation device for X-ray critical dimension measurement provided by an embodiment of the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not constitute a conflict with each other.

Embodiment one

A nanostructure scattering field calculation method 10 for X-ray critical dimension measurement, as shown in Figure 1, comprising:

110. Describe the area enclosed by the curve located in the XOZ coordinate system and the X coordinate axis of the XOZ coordinate system as the cross-sectional profile of the periodic unit of the nanostructure, where the X coordinate axis represents the periodic arrangement of the periodic unit of the nanostructure in the physical space The direction of the cloth, the Z coordinate axis of the XOZ coordinate system represents the direction perpendicular to the substrate plane where the nanostructure is located; the above curve is generated by selecting points in the XOZ coordinate system;

120. Through non-uniform fast Fourier transform, calculate the reciprocal space value of the cross-sectional profile at a specific coordinate position in the reciprocal space, and use it as the shape factor of the nanostructure;

130. Calculating the scattering field of nanostructures for X-ray critical dimension measurement using shape factors.

This embodiment proposes a new section profile description method. A curve is established in the XOZ coordinate system. The curve is generated by selecting points in the XOZ coordinate system. The curve located in the XOZ coordinate system and the X coordinate axis of the XOZ coordinate system The enclosed area is described as the cross-sectional profile of the periodic unit of the nanostructure. This method can avoid the problems of difficulty in modeling and poor fitting caused by the existing description of the cross-sectional profile of the nanostructure only through the superposition of simple geometric shapes.

In addition, after the accurate description of the cross-sectional profile of the periodic unit of the nanostructure, the calculation of the reciprocal space of the nanostructure can be realized by the fast Fourier transform. However, the fast Fourier transform can only be used in the case of equal interval sampling, not It is suitable to describe all cross-sectional information of complex structures, and another method needs to be found. When analyzing complex nanostructures, in order to reduce computational complexity and improve computational efficiency, a method that can achieve non-uniform sampling and calculate the light intensity distribution at a given reciprocal space coordinate is needed. This embodiment adopts a non-uniform fast Fourier transform method to realize spatial numerical calculation. To sum up, the method of this embodiment can avoid the problems of difficulty in modeling and poor fitting caused by describing the cross-sectional profile of the nanostructure only by superposition of simple geometric shapes, and can be applied to nanostructures of different cross-sectional shapes.

Preferably, the above-mentioned curve is formed by selecting control points in the XOZ coordinate system and adopting a cubic uniform B-spline curve method, wherein the above-mentioned selection is randomly selected or selected according to needs.

Cubic uniform B-splines is a method of generating splines from the coordinates of control points, which has the advantage of second-order continuity. As long as the positions of the control points are selected flexibly, curve segments with various characteristics can be obtained. From n+1 control points, n-2 cubic uniform B-spline curve segments can be constructed. Wherein, every four adjacent vertices P _i , P _i+1 , P _i+2 , P _i+3 can define a curve segment Q _i+1 (u), (i=0, . . . , n−3). This section of spline curve can be calculated by the following formula: Q _i+1 (u)=U·M·P, where U=[u ³ u ² u 1],

The method for calculating the scattering field of any surface-shaped nanostructures provided in this embodiment for X-ray critical dimension measurement can be applied to nanostructures with different surface shapes, and the cross-section of the periodic unit generated by B-spline curve control is the most complicated, and its general The degree of automation is also the highest, and the number of control points can be flexibly adjusted according to the accuracy requirements. Taking the grating whose periodic unit section is a B-spline curve as an example, a cubic uniform B-spline curve is used to describe the periodic unit section of the grating, and the area enclosed by the cubic uniform B-spline curve and the X axis is the periodic unit to be simulated section. As shown in Figure 2, in this example, 11 points are selected to control the generated eight-segment B-spline curve to form a grating section, and the control grating scattering field map is shown in Figure 3.

Preferably, the above-mentioned curve is determined by selecting the number of items of the polynomial and the coefficient of each item, wherein the above-mentioned selection is randomly selected or selected according to needs.

That is to say, in addition to using cubic uniform B-spline curves, polynomial curves can also be used to describe the section of periodic elements. For example, if an m-1 degree polynomial with m coefficients is selected, the section profile curve of the periodic unit is calculated by the following formula:

The section of the periodic unit is the area surrounded by the curve and the X-axis, which realizes the flexible description of the section of the periodic unit.

Preferably, the above-mentioned specific coordinate position is obtained in the following manner:

According to the position of the detector, the pixel size of the detector and the incident angle relative to the sample when the actual X-rays irradiate the sample, the reciprocal space coordinate corresponding to the scattered field signal collected actually is calculated as the specific coordinate position.

When measuring nanostructure information at the X-ray critical dimension, it is necessary to reversely guide the nanostructure description in the scattering field simulation based on the actually measured scattering signal to determine the nanostructure information. Part of the coordinate position in the reciprocal space, so this embodiment needs to determine the part of the coordinate position. The specific determination method is: according to the experimental conditions, including information such as the detector position and parameters, and the incident angle, calculate the corresponding reciprocal space coordinates. The position and parameters of the detector determine the amount and quality of the reciprocal spatial information of the nanostructure that can be collected. As shown in Figure 4, the scattering vector corresponding to the scattered light intensity information collected by the detector can be expressed as:

其中，θ为散射角的一半，

where θ is half of the scattering angle,

Among them, SDD is the distance from the sample to the detector, Δa is the distance between a point on the detector and the center of the beam, Δa=n Pixel-Pixel _center , Pixel _center is the detector pixel position where the center of the beam on the detector is located, and Pixel is the detection The pixel size of the detector, n is the pixel number of a certain point of the detector.

In the actual experiment, multiple incident angles are adjusted to obtain multiple sets of information, and the scattering vector is projected on the sample coordinate system to obtain the distribution map of the reciprocal space of the nanostructure. Under a certain incident angle ω, the corresponding scattering vector of the sample along the x and z directions can be calculated as follows:

In general, the implementation flow chart of the method for calculating the scattering field of any surface nanostructure for X-ray critical dimension measurement provided in this embodiment can be shown in Figure 5:

Step 1, establish the calculation model of scattered field for X-ray critical dimension measurement, which can be expressed as the sum of the product of shape factor, structure factor and other factors and background scattering. The calculation model of the scattered field can be expressed as:

Among them, q _x and q _z are the components of the scattering vector q along the x and z directions respectively, I(q _x , q _z ) is the light intensity value corresponding to the scattering vector, N _p is the number of participating scatterers, and ρ is the nanometer Structural electron density distribution, F(q _x ,q _z ) is shape factor, S(q _x ,q _z ) is interference factor (also called structure factor), σ _DWF is roughness influencing factor, I ₀ is scaling factor, I _bkg is the background scattering intensity.

Step 2, describe the periodic unit of any surface nanostructure by polynomial or other methods. The technical solution and the corresponding beneficial effects are specifically the same as those described above.

Step 3. Calculate the corresponding reciprocal space coordinates according to the experimental conditions, including information such as the position and parameters of the detector, and the incident angle.

Step 4, using the non-uniform fast Fourier transform method to calculate the distribution of the periodic unit section at the corresponding reciprocal space coordinates, that is, the shape factor of the nanostructure;

The general formula for calculating the shape factor is:

F(q) = ρ∫e ^{-iq r} dV;

where F(q) is the shape factor of any planar nanostructure, ρ is the electron density of the structure, and dV is the volume differential of the scatterer at r. Taking the grating structure of any surface type as an example, the shape factor calculation formula can be reduced to:

Among them, A is the cross-section of the grating structure, q _x and q _z are the components of the scattering vector along the x and z directions, respectively, and the visible shape factor can be obtained by calculating the two-dimensional Fourier transform of the electron density of the cross-section of the periodic unit of the nanostructure.

The non-uniform fast Fourier transform method can calculate the Fourier transform result at a given frequency domain point by numerical method. When using the NFT method to calculate the shape factor at a given scattering vector position, the frequency domain points of the scattering vector and NFT are not equal, but there is the following corresponding quantitative relationship:

f _x =q _x /2π, f _z =q _z /2π;

Step 5, finally calculating the structure factor of the nanostructure, and combining with other factors such as roughness to obtain the distribution of the X-ray scattering field.

The formula for calculating the structure factor is:

For 1D periodic nanostructures, the structure factor can be reduced to a 1D comb function, namely:

The description and calculation method of other arbitrary surface nanostructures and their shape factors are similar to the implementation process of B-spline curve control to generate grating sections, only need to use the corresponding description and calculation methods for specific grating sections.

Embodiment two

A nanostructure scattered field calculation device 20 for X-ray critical dimension measurement, as shown in Figure 6, comprising:

The cross-sectional profile description module 210 is used to describe the area enclosed by the curve in the XOZ coordinate system and the X-coordinate axis in the XOZ coordinate system as the cross-sectional profile of the periodic unit of the nanostructure, wherein the X-coordinate axis represents the period of the nanostructure The direction in which the units are periodically arranged in the physical space, the Z coordinate axis in the XOZ coordinate system represents the direction perpendicular to the substrate plane where the nanostructure is located; the above curve is calculated by selecting points in the XOZ coordinate system;

The calculation module 220 is used to calculate the reciprocal space value of the cross-sectional profile at a specific coordinate position in the reciprocal space through the non-uniform fast Fourier transform, as the shape factor of the nanostructure; and use the shape factor to calculate the X-ray key Nanostructured Scattering Fields for Size Measurements.

Preferably, the above-mentioned curve is determined by selecting the number of items of the polynomial and the coefficient of each item, wherein the above-mentioned selection is randomly selected or selected according to needs.

Preferably, the above-mentioned curve is determined by selecting the number of items of the polynomial and the coefficient of each item, wherein the above-mentioned selection is randomly selected or selected according to needs.

Preferably, the above-mentioned specific coordinate position is obtained in the following manner:

According to the position of the detector, the pixel size of the detector and the incident angle relative to the sample when the actual X-rays irradiate the sample, the reciprocal space coordinate corresponding to the scattered field signal collected actually is calculated as the specific coordinate position.

For the content not detailed in the device 20 provided in the embodiment of the present application, you can refer to the method 10 provided in the first embodiment above. The beneficial effect that the device 20 provided in the embodiment of the present application can achieve is the same as that of the method 10 provided in the above embodiment. , which will not be repeated here.

Embodiment three

A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for calculating the scattering field of nanostructures for X-ray critical dimension measurement as described above is realized. The relevant technical solutions are the same as those in Embodiment 1, and will not be repeated here.

Embodiment four

An electronic device, comprising: a processor, a transceiver, and the computer-readable storage medium as described above, wherein the transceiver is used to send and receive data under the control of the processor; the processor executes the computer-readable storage medium The computer program on the computer implements the steps of a method for calculating the scattering field of nanostructures for X-ray critical dimension measurement as described above. The relevant technical solutions are the same as those in Embodiment 1, and will not be repeated here.

It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, All should be included within the protection scope of the present invention.

Claims (10)

1. A method for calculating a nanostructure scatter field for X-ray critical dimension measurement, comprising:

describing a region surrounded by a curve in an XOZ coordinate system and an X coordinate axis of the XOZ coordinate system as a section outline of a periodic unit of the nano structure, wherein the X coordinate axis represents a direction in which the periodic unit of the nano structure is periodically arranged in a physical space, and the Z coordinate axis of the XOZ coordinate system represents a direction vertical to a substrate plane in which the nano structure is positioned; the curve is generated through point selection calculation in the XOZ coordinate system;

calculating a reciprocal space value of the section contour at a specific coordinate position in a reciprocal space through non-uniform fast Fourier transform, wherein the reciprocal space value is used as a shape factor of the nano structure;

and calculating the nanostructure scattering field of the X-ray key size measurement by adopting the shape factor.

2. The method of claim 1, wherein the curve is formed by selecting control points in the XOZ coordinate system and using a spline curve method, wherein the selection is random or on demand.

3. The method of claim 1, wherein the curve is determined by selecting the number of terms of a polynomial and the coefficients of each term, wherein the selection is random or on demand.

4. The method of claim 1, wherein the specific coordinate position is obtained by:

and calculating reciprocal space coordinates corresponding to actually collected scattered field signals according to the position of the detector, the size of the pixel of the detector and the incidence angle relative to the sample when the sample is irradiated by the actual X-ray, and taking the reciprocal space coordinates as the specific coordinate position.

5. A nanostructure scattered field calculation apparatus for X-ray critical dimension measurement, comprising:

the cross section outline description module is used for describing an area surrounded by a curve in an XOZ coordinate system and an X coordinate axis in the XOZ coordinate system as the cross section outline of the nanostructure periodic unit, wherein the X coordinate axis represents the periodic arrangement direction of the nanostructure periodic unit in an entity space, and the Z coordinate axis in the XOZ coordinate system represents the direction vertical to a substrate plane where the nanostructure is positioned; the curve is generated through point selection calculation in the XOZ coordinate system;

the calculation module is used for calculating a reciprocal space value of the section outline at a specific coordinate position in a reciprocal space through non-uniform fast Fourier transform, and the reciprocal space value is used as a shape factor of the nano structure; and calculating the nanostructure scattering field of the X-ray critical dimension measurement by adopting the shape factor.

6. The nanostructured fringe field calculating apparatus of claim 5, wherein the curve is formed by selecting control points in the XOZ coordinate system and using a spline curve method, wherein the selection is random or on demand.

7. The nanostructure fringe field calculation apparatus of claim 5, wherein the curve is determined by selecting a number of terms of a polynomial and a coefficient of each term, wherein the selection is random or on demand.

8. The nanostructure fringe field calculation device of any one of claims 5-7, wherein the specific coordinate position is obtained by:

and calculating reciprocal space coordinates corresponding to actually collected scattered field signals according to the position of the detector, the size of the pixel of the detector and the incidence angle relative to the sample when the sample is irradiated by the actual X-ray, and taking the reciprocal space coordinates as the specific coordinate position.

9. A computer-readable storage medium, storing a computer program, wherein the computer program, when executed by a processor, implements a method of nanostructure scatter field calculation for X-ray critical dimension measurement according to any of claims 1-4.

10. An electronic device, comprising: a processor, a transceiver, and a computer-readable storage medium according to claim 9,

the transceiver is used for transceiving data under the control of the processor;

the processor, when executing the computer program on the computer readable storage medium, performs the steps of a method for nanostructure scattered field calculation for X-ray critical dimension measurement according to any of claims 1-5.

Images