CN114593700B - Nano-structure scattered field calculation method for X-ray key size measurement - Google Patents
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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
Technical Field
The invention belongs to the field of X-ray key dimension measurement methods, and particularly relates to a nanostructure scattering field calculation method for X-ray key dimension measurement.
Background
The basic principle of the method is that a beam of collimated X-ray is irradiated on a sample, reciprocal space information of the sample is obtained by measuring a scattering signal of the sample in a small angle range, and then information of the sample to be measured is extracted from the reciprocal space information.
In recent years, due to the increasing complexity of nanostructures, conventional small angle scattering analysis has failed to meet the need for reconstruction of sample information. Therefore, the X-ray critical dimension measurement method changes the incident angle with respect to the incident light by rotating the sample to obtain more comprehensive reciprocal spatial information. However, in the simulation using the X-ray critical dimension measurement method, since the actually manufactured nanostructure tends to have a very complicated shape, there is a need for a method that can accurately describe the periodic unit of the nanostructure and can accurately calculate the shape factor thereof.
The description of the nanostructure periodic element is mainly represented by the superposition of a plurality of basic shapes. The literature (Bernard Cross. Form factor of any polyhedron: a general composition for use and its dimensions. J. Appl. Cryst. (2017). 50, 1245-1255) gives a formula for the calculation of any polyhedral shape factor. Taking a grating as an example, the X-ray critical dimension measurement method uses a plurality of trapezoids superimposed to approximate the actual grating profile. However, the actually manufactured grating cannot be described by an ideal geometric figure, and the existence of roughness makes the description of the cross-sectional profile by an analytic method more difficult to realize. Therefore, careful consideration and analysis are necessary to accurately describe the cross-sectional profile of the periodic unit of the nanostructure and calculate the fringe field information.
Disclosure of Invention
Aiming at the defects and the improvement requirement of the prior art, the invention provides a nanostructure scattered field calculation method for X-ray critical dimension measurement, which aims to solve the problems of difficult modeling and poor fitting degree caused by the fact that the prior art can only describe the section profile of a nanostructure through simple geometric superposition.
To achieve the above object, according to an aspect of the present invention, there is provided a nanostructure scattered field calculation method for X-ray critical dimension measurement, comprising:
describing a region surrounded by a curve located in an XOZ coordinate system and an X coordinate axis of the XOZ coordinate system as a cross-sectional profile of a nanostructure periodic unit, wherein the X coordinate axis represents a direction in which the nanostructure periodic units are periodically arranged in an entity space, and the Z coordinate axis of the XOZ coordinate system represents a direction vertical to a substrate plane in which the nanostructures are located; 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.
Further, 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 as desired.
Further, the curve is determined by selecting the number of terms of the polynomial and the coefficient of each term, wherein the selection is random or as desired.
Further, 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.
The invention also provides a nanostructure scattered field calculation device for X-ray critical dimension measurement, comprising:
the cross-section outline description module is used for describing a region 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 X-ray critical dimension measurement by using the shape factor.
Further, 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 as desired.
Further, the curve is determined by selecting the number of terms of the polynomial and the coefficient of each term, wherein the selection is random or as desired.
Further, 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 when the sample is irradiated by the actual X-ray, the size of the pixel of the detector and the incident angle relative to the sample, and taking the reciprocal space coordinates as the specific coordinate position.
The invention also provides a computer-readable storage medium storing a computer program which, when executed by a processor, implements a nanostructure scattered field calculation method for X-ray critical dimension measurement as described above.
The present invention also provides an electronic device, comprising: a processor, a transceiver, and a computer-readable storage medium as described above, wherein,
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, implements the steps of a nanostructure scattered field calculation method for X-ray critical dimension measurement as described above.
Generally, by the above technical solution conceived by the present invention, the following beneficial effects can be obtained:
(1) The invention provides a novel cross-section profile description mode, wherein a curve is established in an XOZ coordinate system, the curve is generated by selecting points in the XOZ coordinate system through calculation, and an area defined by the curve in the XOZ coordinate system and an X coordinate axis of the XOZ coordinate system is described as the cross-section profile of a periodic unit of a nano structure.
(2) The invention provides a method for calculating the light intensity distribution at a given reciprocal space coordinate by adopting a method capable of realizing non-uniform sampling, and the precision is improved.
(3) The invention adopts a polynomial or spline curve to establish a curve for describing the profile of the cross section, and can flexibly adjust the number of sampling points according to the precision requirement.
In conclusion, the method of the invention can be suitable for the simulation and optimization requirements of the X-ray critical dimension method of the complex nano structure.
Drawings
FIG. 1 is a block diagram of a flow chart of a method for calculating a scattering field of a nanostructure for X-ray critical dimension measurement according to an embodiment of the present invention;
FIG. 2 is a cross-sectional view of a grating controlled by a cubic uniform B-spline curve provided by an embodiment of the present invention;
FIG. 3 is a graph of a grating fringe field controlled by a cubic uniform B-spline curve provided by an embodiment of the present invention;
FIG. 4 is a schematic diagram of an X-ray critical dimension method provided by an embodiment of the present invention;
FIG. 5 is a flowchart of a method for computing a scattering field of a nanostructure of arbitrary surface type in an X-ray critical dimension method based on non-uniform fast Fourier transform according to an embodiment of the present invention;
FIG. 6 is a schematic structural diagram of a device for calculating a scattering field of a nanostructure for X-ray critical dimension measurement according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Example one
A nanostructure scattered field calculation method 10 for X-ray critical dimension measurement, as shown in fig. 1, comprising:
110. describing a region surrounded by a curve located in an XOZ coordinate system and an X coordinate axis of the XOZ coordinate system as a section outline of the 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 of the XOZ coordinate system represents the direction vertical to a substrate plane where the nano structure is located; the curve is generated by selecting points in an XOZ coordinate system;
120. 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;
130. the nanostructure scattering field for X-ray critical dimension measurements was calculated using the shape factor.
The embodiment provides a new cross-sectional profile description mode, a curve is established in an XOZ coordinate system, the curve is generated by selecting points in the XOZ coordinate system through calculation, and a region defined by the curve in the XOZ coordinate system and an X coordinate axis of the XOZ coordinate system is described as a cross-sectional profile of a nanostructure periodic unit.
In addition, after the section outline of the periodic unit of the nano structure is accurately described, the calculation of the reciprocal space of the nano structure can be realized in a fast Fourier transform mode, but the fast Fourier transform can only be used for the condition of equal-interval sampling, is not suitable for describing all section information of a complex structure, and needs to find another method. When analyzing a complex nanostructure, in order to reduce the computational complexity and improve the computational efficiency, a method capable of realizing non-uniform sampling and calculating the light intensity distribution at a given reciprocal space coordinate is required. In this embodiment, a non-uniform fast fourier transform method is used to implement spatial numerical computation. In conclusion, the method of the embodiment can avoid the problems of difficult modeling and poor fitting degree caused by the fact that the cross section profile of the nano structure can only be described by simple geometric shape superposition in the prior art, and can be suitable for nano structures with different cross section shapes.
Preferably, the curve is formed by selecting control points in the XOZ coordinate system and using a cubic uniform B-spline curve method, wherein the selection is random or as desired.
The cubic uniform B-spline curve is a method for generating a spline curve through the coordinates of control points and has the advantage of second-order continuity. The curve segments with various characteristics can be obtained by flexibly selecting the positions of the control points. N-2 cubic uniform B-spline curve segments can be constructed from n +1 control points. Wherein, every adjacent four vertexes P i ,P i+1 ,P i+2 ,P i+3 A curve section Q can be defined i+1 (u), (i =0, \8230;, n-3). The spline curve can be calculated by: q i+1 (U) = U · M · P, where U = [ U ] 3 u 2 u 1]，
The method for calculating the scattering field of the optional-surface type nano structure for measuring the critical dimension of the X-ray can be suitable for nano structures with different surface types, wherein the periodic unit section generated by controlling the B-spline curve is the most complex, the generalization degree of the periodic unit section is the highest, and in addition, the number of control points can be flexibly adjusted according to the precision requirement. The grating with the periodic unit cross section as a B-spline curve is taken as an embodiment, the periodic unit cross section of the grating is described by a cubic uniform B-spline curve, and a region enclosed by the cubic uniform B-spline curve and an X axis is the periodic unit cross section to be simulated. As shown in FIG. 2, the eight B-spline curves generated by selecting 11 points to control in this example constitute the grating cross section, and the controlled grating fringe field pattern is shown in FIG. 3.
Preferably, the curve is determined by selecting the number of terms of the polynomial and the coefficient of each term, wherein the selection is random or as desired.
That is, the periodic unit cross section can be described by using a polynomial curve or the like in addition to the cubic uniform B-spline curve. For example, an m-1 th order polynomial is selected containing m coefficients, and the periodic cell cross-sectional profile curve is calculated by:
the section of the periodic unit is an area formed by the curve and an X axis in a surrounding mode, and flexible description of the section of the periodic unit is achieved.
Preferably, 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.
When measuring nanostructure information in an X-ray critical dimension, it is necessary to guide a description of a nanostructure in a fringe field simulation backward according to an actually measured scattering signal to determine the nanostructure information, where the actually measured scattering signal is only a partial coordinate position of the nanostructure in a reciprocal space, and therefore, the present embodiment determines the partial coordinate position in a specific determination manner: and calculating corresponding reciprocal space coordinates according to experimental conditions including information such as the position and parameters of the detector, the incident angle and the like. The location and parameters of the detector determine the amount and quality of the nanostructure reciprocal space information that can be collected. As shown in fig. 4, the scattering vector corresponding to the scattered light intensity information collected by the detector can be represented as:
where SDD is the distance from the sample to the detector, Δ a is the distance from a point on the detector to the center of the beam, Δ a = n · Pixel-Pixel center ，Pixel center The Pixel position of the detector where the center of the light beam on the detector is located, pixel is the size of the detector Pixel, and n is the Pixel sequence number of a certain point of the detector.
In an actual experiment, a plurality of incident angles are adjusted to obtain a plurality of groups of information, and the scattering vectors are projected on a sample coordinate system to obtain a distribution diagram of the reciprocal space of the nano structure. At a certain angle of incidence ω, the scattering vector of the sample along the x, z directions can be calculated as follows:
in summary, the flow chart of the method for calculating the scattering field of the arbitrary-surface type nanostructure for X-ray critical dimension measurement according to the present embodiment can be shown in fig. 5:
step 1, establishing a scattered field calculation model of X-ray key size measurement, wherein the model can be expressed as the sum of the product of shape factors, structural factors and other factors and background scattering. The scatter field calculation model can be expressed as:
wherein q is x And q is z The components of the scattering vector q in the x and z directions, I (q), respectively x ,q z ) For the light intensity value, N, corresponding to the scattering vector p ρ is the nanostructure electron density distribution, F (q), the number of participating scatterers x ,q z ) Is a form factor, S (q) x ,q z ) Is the interference factor (also called the structure factor), σ DWF As a factor affecting roughness, I 0 Is a scale factor, I bkg Background scattering intensity.
And 2, describing periodic units of the random-face nano structure by a polynomial or other methods. The technical scheme and the corresponding beneficial effects are specifically as described above.
And 3, calculating corresponding reciprocal space coordinates according to experimental conditions including information such as the position and parameters of the detector, the incident angle and the like.
Step 4, calculating the distribution of the section of the periodic unit at the position corresponding to the reciprocal space coordinate by adopting a non-uniform fast Fourier transform method, namely the shape factor of the nano structure;
the general calculation formula for the shape factor is:
F(q)＝ρ∫e -iq·r dV；
where F (q) is the shape factor of the arbitrary-face 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:
wherein A is the cross section of the grating structure, q x And q is z The components of the scattering vector along the x direction and the z direction are respectively, and the visible shape factor can be obtained by two-dimensional Fourier transform calculation of the electron density of the section of the periodic unit of the nano structure.
The non-uniform fast fourier transform method may compute the fourier transform result at a given frequency domain point by a numerical method. When calculating the shape factor at a given scattering vector position using the non-uniform fast fourier transform method, the frequency domain points of the scattering vector and the non-uniform fast fourier transform are not equal, but there is the following correspondence quantity relationship:
f x ＝q x /2π,f z ＝q z /2π；
and 5, finally, calculating the structural factor of the nano structure, and combining other factors such as roughness and the like to obtain the distribution of the X-ray scattering field.
The formula for calculating the structural factor is as follows:
for one-dimensional periodic nanostructures, the structure factor can be simplified to a one-dimensional comb function, i.e.:
the description of other arbitrary surface type nano structures and the calculation method of the shape factor thereof are similar to the implementation process of generating the grating section by controlling the B spline curve, and only the specific grating section needs to adopt the corresponding description and calculation method.
Example two
A nanostructure scattered field calculation apparatus 20 for X-ray critical dimension measurement, as shown in fig. 6, comprising:
a cross-section profile description module 210, configured to describe, as a cross-section profile of the nanostructure cycle unit, a region surrounded by a curve in an XOZ coordinate system and an X coordinate axis in the XOZ coordinate system, where the X coordinate axis represents a direction in which the nanostructure cycle units are periodically arranged in an entity space, and the Z coordinate axis in the XOZ coordinate system represents a direction perpendicular to a substrate plane where the nanostructures are located; the curve is generated by selecting points in an XOZ coordinate system;
the calculating module 220 is configured to calculate a reciprocal space value of the cross-sectional profile at a specific coordinate position in a reciprocal space through non-uniform fast fourier transform, where the reciprocal space value is used as a shape factor of the nanostructure; and calculating the nanostructure scattering field of the X-ray critical dimension measurement by adopting the shape factor.
Preferably, the curve is determined by selecting the number of terms of the polynomial and the coefficient of each term, wherein the selection is random or as desired.
Preferably, the curve is determined by selecting the number of terms of the polynomial and the coefficient of each term, wherein the selection is random or as desired.
Preferably, 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 when the sample is irradiated by the actual X-ray, the size of the pixel of the detector and the incident angle relative to the sample, and taking the reciprocal space coordinates as the specific coordinate position.
For the content that is not described in detail in the apparatus 20 provided in the embodiment of the present application, reference may be made to the method 10 provided in the first embodiment, and the beneficial effects that the apparatus 20 provided in the embodiment of the present application can achieve are the same as the method 10 provided in the embodiment described above, and are not described again here.
EXAMPLE III
A computer-readable storage medium storing a computer program which, when executed by a processor, implements a nanostructure scattered field calculation method for X-ray critical dimension measurement as described above. The related technical solution is the same as the first embodiment, and is not described herein again.
Example four
An electronic device, comprising: a processor, a transceiver, and a computer readable storage medium as described above, wherein the transceiver is configured to transceive data under control of the processor; a processor, when executing the computer program on the computer readable storage medium, implements the steps of a method for nanostructure scatter field calculation for X-ray critical dimension measurement as described above. The related technical solution is the same as the first embodiment, and is not described herein again.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the 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.
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| Anomalous small-angle X-ray scattering (ASAXS) study of irradiation-induced nanostructure change in Fe-ion beam irradiated oxide dispersion-strengthened (ODS) steel;TakayukiKumada;《Journal of Nuclear Materials》;20200130;全文 * |
| 基于SAXS的不同变质程度煤纳米级孔隙结构特征研究;张钰;《煤田地质与勘探》;20210630;全文 * |
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