Overlay error measurement method and system based on x-ray incident angle optimization

Abstract

The application belongs to the field of overlay error measurement, and particularly discloses an overlay error measurement method and system based on X-ray incident angle optimization, which comprises the following steps: based on X-ray scattering field modeling, determining the relationship between the overlay error of an overlay structure and the scattering intensity; then obtaining the approximate linear relationship between the relative difference between the overlay structure and the ideal double-layer nanostructure scattering intensity and the overlay error; based on a pair of overlay structures with positive and negative offset amounts, determining the approximate mapping model of the scattering intensity of the pair of overlay structures and the overlay error according to the approximate linear relationship; using X-rays with different incident angles to perform simulation, obtaining the corresponding scattering intensity, calculating the overlay error according to the approximate mapping model, and determining the optimal incident angle according to the overlay error accuracy; and using the optimal incident angle to measure the overlay structure to obtain the overlay error. The application can solve the problems of slow measurement speed, multiple steps and complex data processing in overlay error measurement.

Description

Technical Field

[0001] This invention belongs to the field of overlay error measurement, and more specifically, relates to an overlay error measurement method and system based on X-ray incident angle optimization. Background Technology

[0002] Overlay error is a very important parameter in integrated circuit manufacturing. It reflects the alignment accuracy between the current lithography process layer and the previous lithography process layer. It is directly related to the precision control of critical dimensions, process consistency and device performance optimization. Its rapid measurement and evaluation are key to process optimization.

[0003] Existing methods for measuring overlay error are mainly based on optical imaging or non-imaging diffraction. Optical imaging-based methods directly observe the overlay marks in the nanostructure using imaging equipment (such as a microscope) and measure their positional offset between two process layers. This method has the advantages of low equipment cost and fast measurement speed. However, due to limitations in optical resolution, microscopes may not be sufficient for measuring small-sized, complex integrated circuits. Optical diffraction (scattering measurement) is another commonly used method for measuring overlay error. By analyzing the diffraction or scattering phenomena caused by the interaction between incident light and the overlay marks, and analyzing the intensity, phase, or direction of the diffracted or scattered light, information about the overlay error can be inferred. Optical diffraction methods can achieve rapid, non-destructive measurements and are suitable for large-area overlay error assessment. However, it has high requirements for the surface morphology and optical properties of the sample.

[0004] As semiconductor devices become smaller and their structures more complex, diffraction-based measurement methods have been extended to short-wavelength X-rays, leading to X-ray scattering-based nanostructure measurement technology. Patent CN107533020A discloses a computationally efficient X-ray-based overlay error measurement method, pointing out that when scanning along the incident angle, overlay error causes an approximately linear shift in the position of the minimum value of the scattering curve. Therefore, a linear mapping relationship between the minimum value position shift and the overlay error can be established to measure the overlay error. Patent CN115790469A discloses a method and apparatus for measuring integrated circuit overlay error based on small-angle X-ray scattering, deriving this approximately linear relationship. However, existing methods require multi-incident-angle measurements, resulting in long measurement times and high measurement complexity.

[0005] Therefore, there is an urgent need for a simple and fast measurement method for overlay error measurement to solve the above-mentioned problems in the existing technology. Summary of the Invention

[0006] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method and system for measuring overlay error based on X-ray incident angle optimization. Its purpose is to achieve high-precision extraction of overlay error with simple measurement configuration and fast measurement speed.

[0007] To achieve the above objectives, according to a first aspect of the present invention, a method for measuring overlay error based on X-ray incident angle optimization is proposed, comprising the following steps:

[0008] S1. Based on X-ray scattering field modeling, determine the relationship between the overlay error of the overlay structure and the scattering intensity;

[0009] S2. Based on the relationship between the overlay error and scattering intensity of the overlay structure, an approximate linear relationship is obtained between the relative difference in scattering intensity between the overlay structure and the ideal double-layer nanostructure and the overlay error.

[0010] S3. Set up a pair of overlay structures with upper and lower layer offsets of δ+D and δ-D, and a pair of ideal double-layer nanostructures with corresponding upper and lower layer offsets of +D and -D, where δ is the overlay error; substitute the scattering intensity corresponding to the two pairs of structures into the approximate linear relationship to obtain an approximate mapping model between the scattering intensity of the overlay structure and the overlay error.

[0011] S4. Simulate using X-rays with different incident angles to obtain the corresponding scattering intensity, and then calculate the overlay error based on the approximate mapping model. Determine the optimal X-ray incident angle based on the accuracy of the overlay error.

[0012] S5. The overlay structure to be measured is measured using the optimal X-ray incident angle to obtain the overlay error.

[0013] As a further preferred option, in step S1, the relationship between the overlay error and the overlay structure shape factor is first determined, and then the scattering intensity is taken as the square of the overlay structure shape factor modulus.

[0014] As a further preferred embodiment, in step S1, the relationship between the overlay error of the overlay structure and the scattering intensity is as follows:

[0015] P(q x ,q z )=|F| 2 [(Δρ1+Δρ2cos Z) 2 +(Δρ2sin Z) 2 ]

[0016] Where P(q) x ,q z ) represents the scattering intensity of the overlay structure; Δρ1 represents the electron density difference between the lower structure and the filling layer; Δρ2 represents the electron density difference between the upper structure and the air layer; q x and q zLet X be the components of the scattering vector along the X and Z directions, where X is the periodic direction of the overlay structure and Z is the height direction of the overlay structure; S is the vertical distance between the lower and upper structures, and F is the shape factor of a single-layer cross-section of the overlay structure.

[0017] As a further preferred embodiment, in step S2, the approximate linear relationship is:

[0018]

[0019] Wherein, P0(q) x ,q z Y = q represents the scattering intensity of an ideal double-layer nanostructure without overlay error. z S, A=Δρ1+Δρ2cos Y, B=Δρ2sin Y.

[0020] As a further preferred embodiment, in step S3, the approximate mapping model is:

[0021]

[0022]

[0023]

[0024]

[0025] Among them, P + ,P - The scattering intensities of the overlay structures offset by δ+D and δ-D, respectively, are the upper and lower layers; A + =Δρ1+Δρ2cos M,B + =Δρ2sin M,A - =Δρ1+Δρ2cos N,B - =Δρ2sin N; M=+q x D+q z S,N=-q x D+q z S.

[0026] As a further preferred step, in step S4, for a certain incident angle, the scattering intensity under N preset overlay errors is obtained by simulation, and then N extraction overlay errors are calculated according to the approximate mapping model. Based on the deviation between the N preset overlay errors and the extraction overlay errors, the incident angle with the smallest deviation is selected as the optimal X-ray incident angle.

[0027] As a further preferred embodiment, in step S4, the calculation method for the deviation MSE between the preset overlay error and the extracted overlay error is as follows:

[0028]

[0029] Where, δ input,i For the i-th preset overlay error, δ extracted,i Let be the i-th extraction overlay error.

[0030] According to a second aspect of the present invention, a system for measuring overlay error based on X-ray incident angle optimization is provided, comprising a processor for executing the above-described method for measuring overlay error based on X-ray incident angle optimization.

[0031] According to a third aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the above-described method for measuring overlay error based on X-ray incident angle optimization.

[0032] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages:

[0033] 1. This invention establishes a mapping model between scattering intensity and overlay error. Through experimental configuration optimization, it avoids incident angle scanning and only requires measurement of the overlay sample at a single optimized incident angle, achieving rapid and high-precision overlay error extraction. This solves the problems of slow measurement speed, multiple steps, and complex data processing in current overlay error measurement.

[0034] 2. This invention ingeniously obtains an approximately linear relationship between the relative difference in scattering intensity between the overlay structure and the corresponding ideal structure and the overlay error, and then sets overlay structures with positive and negative biases, thus determining the mapping model between scattering intensity and overlay error; thereby, the accuracy of the overlay error obtained at each incident angle can be quickly determined through simulation, and the incident angle can be quickly optimized to obtain the optimal X-ray incident angle. Attached Figure Description

[0035] Figure 1 This is a flowchart of the overlay error measurement method based on X-ray incident angle optimization according to an embodiment of the present invention;

[0036] Figure 2 This is a schematic diagram illustrating the principle of the nanostructure X-ray scattering measurement method according to an embodiment of the present invention;

[0037] Figure 3 This is a schematic diagram of the overlay nanostructure in an embodiment of the present invention;

[0038] Figure 4 (a) and (b) are schematic diagrams of the overlay structure with positive and negative biases in an embodiment of the present invention;

[0039] Figure 5 This is a schematic diagram showing the approximate mapping relationship between the optimized scattering intensity combination and the overlay error δ in an embodiment of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0041] This invention provides a method for measuring overlay error based on X-ray incident angle optimization, such as... Figure 1 As shown, it includes the following steps:

[0042] S1, based on the principle of X-ray scattering field modeling, such as Figure 2 As shown, the scattering intensity of the overlaid nanostructure is calculated.

[0043] like Figure 3 As shown, the overlay structure includes, from top to bottom, an upper structure, a filling layer, and a lower structure; the shape factor of the overlay structure can be written as:

[0044]

[0045] Where Δρ1=ρ1-ρ2, ρ1 is the electron density of the lower structure, and ρ2 is the electron density of the filled layer; Δρ2=ρ3-ρ0, ρ3 is the electron density of the upper structure, and ρ0 is the electron density of the air layer; q x and q z δ represents the components of the scattering vector along the X and Z directions, where X is the periodic direction of the overlay structure and Z is the height direction of the overlay structure; δ is the overlay error; S is the vertical distance between the lower and upper structures; and F is the shape factor of a single-layer cross-section of the overlay structure.

[0046] Scattering intensity P(q) x ,q z It can be expressed by the following formula:

[0047] P(q x ,q z )=|F(q x ,q z )| 2 =|F| 2 [(Δρ1+Δρ2cos Z) 2 +(Δρ2sin Z) 2 (2)

[0048] Where Z = q x ·δ+q z S.

[0049] S2, calculate the relative difference in scattering intensity between the overlaid nanostructure and the ideal bilayer nanostructure, and obtain its approximate linear relationship with the overlay error.

[0050] In this embodiment, the approximate linear relationship is:

[0051]

[0052] Wherein, P0(q) x ,q z Y = q represents the scattering intensity of an ideal double-layer nanostructure without overlay error. z S, A=Δρ1+Δρ2cos Y, B=Δρ2sin Y.

[0053] S3. Based on a pair of overlay structures with positive and negative biases, the combination of scattering intensities of the pair of overlay structures is calculated according to an approximate linear relationship, resulting in an approximate mapping model between scattering intensity and overlay error.

[0054] like Figure 4 As shown, an overlay structure with upper and lower layer offsets of δ+D and δ-D is set, and an ideal bilayer nanostructure with corresponding upper and lower layer offsets of +D and -D is set.

[0055] Based on the approximate linear relationship, we can obtain:

[0056]

[0057] Among them, P + ,P - P represents the scattering intensity when the upper and lower layers are offset by δ+D and δ-D, respectively. +D ,P -D The values ​​represent the scattering intensities of an ideal bilayer nanostructure with upper and lower layers offset by +D and -D, respectively.

[0058]

[0059] A + =Δρ1+Δρ2cos M,B + =Δρ2sin M,A - =Δρ1+Δρ2cos N,B - =Δρ2sin N; and M=+q x D+q z S,N=-q x D+q z S.

[0060] The scattering intensity relationship of the ideal bilayer nanostructure with upper and lower layer offsets of +D and -D in equation (4) is: P +D / P -D =K3;

[0061] in,

[0062] Combining the above equations, we obtain an approximate mapping model between scattering intensity and overlay error:

[0063]

[0064] S4, based on the approximate mapping model, optimizes the incident angle according to the accuracy of overlay error extraction.

[0065] Specifically, simulations were performed using X-rays at different incident angles. For a given incident angle, the scattering intensity (i.e., P) under a preset overlay error was obtained through simulation. + P - The corresponding extraction overlay error is calculated based on the approximate mapping model. The incident angle with the smallest deviation between the preset overlay error and the extraction overlay error is selected as the optimal X-ray incident angle.

[0066] Furthermore, N preset overlay errors are input during simulation; the deviation MSE between the preset overlay errors and the extracted overlay errors is calculated as follows:

[0067]

[0068] Where, δ input,i δ represents the preset overlay error for the i-th input. extracted,i The calculated overlay error is the i-th error.

[0069] S5 employs the optimal X-ray incident angle, enabling high-precision extraction of overlay errors under this optimal experimental configuration.

[0070] The following are specific examples:

[0071] Measuring integrated circuit overlay errors includes: for example... Figure 3 The trapezoidal overlay structure shown was simulated. Simulation parameters included bottom width w1 = 80 nm, overlay morphology height h = 100 nm, overlay structure period L = 125 nm in the X direction, vertical distance S = 150 nm between the previous layer structure mark and the current layer structure mark, and electron densities ρ1 = 3, ρ2 = 2, ρ3 = 1. Figure 4 As shown, the bias D was set to 20 nm, and the scattering intensity of the first order was used. The overlay error used in the simulation was -10 nm to 10 nm. After optimization, the optimal incident angle was determined to be 39.8°. The relationship between the simulated overlay error and the extracted overlay error is as follows: Figure 5 As shown. Figure 5 This indicates that the linear mapping relationship exists and is quite obvious, and it matches the analytical formula derived in this invention.

[0072] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for measuring overlay error based on X-ray incident angle optimization, characterized in that, Includes the following steps: S1. Based on X-ray scattering field modeling, determine the relationship between the overlay error of the overlay structure and the scattering intensity, specifically: in, The scattering intensity of the overlay structure, and The components of the scattering vector along the X and Z directions are: X direction is the periodic direction of the overlay structure, and Z direction is the height direction of the overlay structure. The difference in electron density between the lower structure and the filling layer. The electron density difference between the upper structure and the air layer is represented by F, where F is the shape factor of the single-layer cross-section of the overlay structure. S is the vertical distance between the lower and upper structures, and δ is the overlay error. S2. Based on the relationship between the overlay error and scattering intensity of the overlay structure, an approximately linear relationship is obtained between the relative difference in scattering intensity between the overlay structure and the ideal bilayer nanostructure and the overlay error, specifically: in, The scattering intensity of an ideal double-layer nanostructure with no overlay error. , , ; S3. Set the upper and lower layer offsets to δ+D, δ A pair of engraved structures of D, and the corresponding upper and lower layer offsets of +D. A pair of ideal bilayer nanostructures of D; substituting the scattering intensities corresponding to the two pairs of structures into the approximate linear relationship, an approximate mapping model of the scattering intensity of the overlay structure and the overlay error is obtained; S4. Simulate using X-rays with different incident angles to obtain the corresponding scattering intensity, and then calculate the overlay error based on the approximate mapping model. Determine the optimal X-ray incident angle based on the accuracy of the overlay error. S5. The overlay structure to be measured is measured using the optimal X-ray incident angle to obtain the overlay error.

2. The overlay error measurement method based on X-ray incident angle optimization as described in claim 1, characterized in that, Step S3, the approximate mapping model is: in, The offsets between the upper and lower layers are δ+D and δ, respectively. The scattering intensity of the D overlay structure; , , , ; .

3. The overlay error measurement method based on X-ray incident angle optimization as described in claim 1 or 2, characterized in that, Step S4: For a certain incident angle, the scattering intensity under N preset overlay errors is obtained by simulation, and then N extraction overlay errors are calculated according to the approximate mapping model. The deviation between the N preset overlay errors and the extraction overlay errors is calculated. The incident angle with the smallest deviation is selected as the optimal X-ray incident angle.

4. The overlay error measurement method based on X-ray incident angle optimization as described in claim 3, characterized in that, Step S4, the calculation method for the deviation MSE between the preset overlay error and the extracted overlay error is as follows: in, For the first i Preset overlay error For the first i Extraction of overlay error.

5. A system for measuring overlay error based on X-ray incident angle optimization, characterized in that, Includes a processor for executing the overlay error measurement method based on X-ray incident angle optimization as described in any one of claims 1-4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the overlay error measurement method based on X-ray incident angle optimization as described in any one of claims 1-4.

Images