CN108693715B - Multi-target light source and mask optimization method for improving full-field photoetching imaging uniformity - Google Patents

Multi-target light source and mask optimization method for improving full-field photoetching imaging uniformity Download PDF

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CN108693715B
CN108693715B CN201810649199.9A CN201810649199A CN108693715B CN 108693715 B CN108693715 B CN 108693715B CN 201810649199 A CN201810649199 A CN 201810649199A CN 108693715 B CN108693715 B CN 108693715B
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李艳秋
李铁
孙义钰
盛乃援
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
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    • G03F7/70425—Imaging strategies, e.g. for increasing throughput or resolution, printing product fields larger than the image field or compensating lithography- or non-lithography errors, e.g. proximity correction, mix-and-match, stitching or double patterning
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Abstract

The invention provides a multi-objective light source and mask optimization method for improving the full-field photoetching imaging uniformity, which constructs an objective function as an average value of point pattern errors of all fields, thereby comprehensively considering the full-field polarization aberration information of a photoetching objective lens in the optimization process. Therefore, the light source and the mask obtained by optimization are not only suitable for photoetching imaging of a specific field-of-view point, but also suitable for photoetching imaging of a full field of view. For the large-field photoetching objective lens containing polarization aberration, the effect is beneficial to improving the full-field photoetching imaging uniformity and ensuring the yield of photoetching process.

Description

Multi-target light source and mask optimization method for improving full-field photoetching imaging uniformity
Technical Field
The invention relates to a multi-target light source and mask optimization method for improving the full-field photoetching imaging uniformity, and belongs to the technical field of photoetching resolution enhancement.
Background
Photolithography is a key technology in the field of very large scale integrated circuit manufacturing. The working wavelength of the deep ultraviolet lithography system which is mainstream in the industry at present is 193nm, and as the node of the lithography process moves down to 45-14 nm, the minimum line width of an integrated circuit is far smaller than the wavelength of a light source. At this time, the interference and diffraction phenomena of the optical wave are more remarkable, which leads to distortion, offset or resolution reduction of the photoetching imaging; therefore, the photolithography system must adopt a resolution enhancement technique to improve the photolithography imaging resolution and the pattern fidelity and ensure the yield of the photolithography process. A light source-mask optimization (SMO) is an important high-freedom lithography resolution enhancement technique, which modulates the amplitude and phase of a mask diffraction spectrum by optimizing the light source intensity distribution and mask transmittance distribution, thereby improving the lithography imaging quality.
At present, for an immersion type projection lithography system with a large field of view, polarization aberrations of lithography objective lenses corresponding to different field of view points are different. Since the polarization aberration is a key factor influencing vector light wave imaging, the difference can cause uneven imaging of each area on the silicon wafer, and the yield of the photoetching process is reduced.
Chinese patent publication No. CN 102269926B proposes an Optical Proximity Correction (OPC) method for a non-ideal lithography system based on a vector imaging model, aiming at polarization aberration of an ultra-high Numerical Aperture (NA) lithography objective lens and defocus error of a lithography system. The method considers the polarization aberration of the ultrahigh NA photoetching objective lens and the defocusing error of the photoetching system, and the mask pattern obtained through optimization is more suitable for the actual photoetching process. However, the method neglects the difference of polarization aberration of different field points of the lithography objective lens, is difficult to give consideration to the uniformity of full-field lithography imaging, and limits the further improvement of the yield of the lithography process.
Sources of lithography objective polarization aberrations include, but are not limited to: scattering at the lens surface, film and crystal birefringence effects. The above factors all cause the change of the intensity, phase and polarization state of the imaging light wave, thereby affecting the imaging resolution and fidelity. In addition, the polarization aberration of the lithography objective lens corresponding to different view points is also different. Therefore, a light source-mask optimization method comprehensively considering the polarization aberration of each field point of the lithography objective lens is needed to compensate the influence of the polarization aberration on the lithography imaging performance and realize uniform lithography imaging in the whole field of view.
Disclosure of Invention
The invention aims to provide a multi-objective light source-mask optimization method under the condition of comprehensively considering the polarization aberration of each field point of a photoetching objective lens.
The technical solution for realizing the invention is as follows:
the invention discloses a multi-target light source and mask optimization method for improving the whole-field photoetching imaging uniformity, which is characterized by comprising the following steps of:
step one, initializing a light source pattern and a mask pattern;
step two, constructing an optimized objective function D:
polarization aberration PA based on lithography objective ith view field point correspondenceiDetermining an imaging fidelity function for an ith field of view point
Figure GDA0001760155540000021
Wherein i is 1,2, n, n is the number of field points;
Figure GDA0001760155540000022
the pixel value of each pixel point of the target graph is taken; z (x, y, PA)i) Presentation taking into account polarization aberrations PAiUnder the condition of (1), calculating the pixel value of each pixel point in the photoresist imaging corresponding to the current light source pattern and the mask pattern by utilizing a photoetching imaging model; the objective function D is constructed as the average value of the imaging fidelity function of each field point of the lithography objective, i.e.
Figure GDA00017601555400000310
And thirdly, optimizing the light source and the mask based on the optimization objective function D.
Preferably, the specific process of the third step is as follows:
step 401, calculating a light source variable matrix omega of the objective function D corresponding to the current light source graphsGradient matrix of
Figure GDA0001760155540000031
Then, an approximation of the gradient matrix is obtained
Figure GDA0001760155540000032
Calculating a mask variable matrix omega corresponding to the target function D to the current mask patternMGradient matrix of
Figure GDA0001760155540000033
Updating the light source variable matrix omega by using the steepest descent methodsIs composed of
Figure GDA0001760155540000034
Obtaining a corresponding current omegasLight source pattern J of (a); updating mask variable matrix omega by using steepest descent methodMIs composed of
Figure GDA0001760155540000035
Wherein
Figure GDA0001760155540000036
Obtaining the corresponding current omega for the preset mask optimization step lengthMThe mask pattern M of (2); updating a binary mask pattern M corresponding to a current mask pattern Mb；
Step 402, calculating the current light source pattern J and the binary mask pattern MbThe value of the corresponding objective function D; when the value is less than the predetermined threshold value or the light source variable matrix omega is updatedsAnd mask variable matrix omegaMWhen the number of times reaches a preset upper limit value, the step 403 is entered, otherwise, the step 401 is returned to;
step 403, terminating the optimization, and combining the current light source pattern J and the binary mask pattern MbAnd determining the optimized light source pattern and mask pattern.
Preferably, the specific process of the first step is as follows:
step 301, initializing the light source to NS×NSThe mask pattern M is initialized to a target pattern of size N × N
Figure GDA0001760155540000037
Wherein N isSAnd N is an integer;
step 302, setting the pixel value of a light-emitting area on the initial light source graph J as 1 and the pixel value of a non-light-emitting area as 0; set size to NS×NSLight source variable matrix omegas: when J (x)s,ys) When the number is equal to 1, the alloy is put into a container,
Figure GDA0001760155540000038
when J (x)s,ys) When the content is equal to 0, the content,
Figure GDA0001760155540000039
wherein J (x)s,ys) Representing a pixel point (x) on the light source patterns,ys) A pixel value of (a); setting the transmissivity of a light transmission area of the initial mask pattern M to be 1 and the transmissivity of a light blocking area to be 0; setting a mask variable matrix Ω of size N × NM: when M (x, y) is 1,
Figure GDA0001760155540000041
when M (x, y) is 0,
Figure GDA0001760155540000042
wherein M (x, y) represents the transmittance of each pixel (x, y) on the mask pattern; let the initial binary mask pattern Mb＝M。
Preferably, the polarization aberration PAiCalculated under the premise of considering the influence of lens surface scattering and film and crystal birefringence effects.
The invention has the following beneficial effects:
the invention constructs the objective function as the average value of the point pattern errors of each field of view, thereby comprehensively considering the full-field polarization aberration information of the photoetching objective lens in the optimization process. Therefore, the light source and the mask obtained by optimization are not only suitable for photoetching imaging of a specific field-of-view point, but also suitable for photoetching imaging of a full field of view. For the large-field photoetching objective lens containing polarization aberration, the effect is beneficial to improving the full-field photoetching imaging uniformity and ensuring the yield of photoetching process.
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FIG. 1 is a flow chart of the optimization method of the present invention.
FIG. 2 is a flowchart of a multi-objective light source-mask optimization method for a non-ideal lithography system according to the present embodiment.
FIG. 3 is a schematic diagram of an initial light source, an initial mask and its corresponding imaging in photoresist.
FIG. 4 is a schematic diagram of a light source pattern, a mask pattern and their corresponding imaging in a photoresist optimized by the related art (CN 102269926B, 2012.08.15).
FIG. 5 is a schematic diagram of a light source pattern, a mask pattern and their corresponding images in a photoresist optimized by the multi-objective light source-mask optimization method of the present invention.
FIG. 6 is a schematic diagram of a light source pattern and a mask pattern optimized for full-field polarization aberration by using the multi-objective light source-mask optimization method provided by the present invention.
Detailed Description
The present invention will be further described in detail with reference to the accompanying drawings.
The principle of the invention is as follows: on the basis of the optimization method of the nonideal photoetching system OPC based on the Abbe vector imaging model, the optimization objective function simultaneously containing the polarization aberration information of each field point of the photoetching objective lens is designed, so that the optimized light source and the optimized mask can obtain a better exposure effect in the full-field range, and the full-field photoetching imaging uniformity is effectively improved.
As shown in fig. 1, a multi-objective light source-mask optimization method for improving the full-field lithography imaging uniformity includes the following specific processes:
step one, initializing a light source pattern and a mask pattern;
step two, constructing an optimized objective function D:
setting F as an imaging fidelity function, and considering polarization aberration PA corresponding to ith field point of the photoetching objective lensiThen, then
Figure GDA0001760155540000051
Wherein
Figure GDA0001760155540000052
Is the pixel value of each pixel point of the target pattern, Z (x, y, PA)i) Presentation taking into account polarization aberrations PAiCalculating the pixel value of each pixel point in the photoresist imaging corresponding to the current light source graph and the mask graph by utilizing a photoetching imaging model; the objective function D is constructed as the average value of the imaging fidelity function of each field point of the lithography objective, i.e.
Figure GDA0001760155540000053
And thirdly, optimizing the light source and the mask based on the objective function.
As shown in fig. 2, the embodiment establishes a multi-objective light source-mask optimization method for full-field polarization aberration, and the specific steps are as follows:
(1) initiating a light sourceChange to size NS×NSThe mask pattern M is initialized to a target pattern of size N × N
Figure GDA0001760155540000054
Wherein N isSAnd N is an integer.
(2) Setting the pixel value of a light-emitting area on the initial light source graph J as 1 and the pixel value of a non-light-emitting area as 0; set size to NS×NSLight source variable matrix omegas: when J (x)s,ys) When the number is equal to 1, the alloy is put into a container,
Figure GDA0001760155540000055
when J (x)s,ys) When the content is equal to 0, the content,
Figure GDA0001760155540000061
wherein J (x)s,ys) Representing each pixel point (x) on the light source patterns,ys) A pixel value of (a); setting the transmissivity of a light transmission area of the initial mask pattern M to be 1 and the transmissivity of a light blocking area to be 0; setting a mask variable matrix Ω of size N × NM: when M (x, y) is 1,
Figure GDA0001760155540000062
when M (x, y) is 0,
Figure GDA0001760155540000063
wherein M (x, y) represents the transmittance of each pixel (x, y) on the mask pattern; let the initial binary mask pattern Mb＝M。
(3) Constructing an optimized objective function D; setting F as an imaging fidelity function, and considering polarization aberration PA corresponding to ith field point of the photoetching objective lensiThen, then
Figure GDA0001760155540000064
Wherein
Figure GDA0001760155540000065
Is the pixel value of each pixel point of the target pattern, Z (x, y, PA)i) Representation taking into account polarization aberrationsPAiCalculating the pixel value of each imaging pixel point in the photoresist corresponding to the current light source graph and the mask graph by utilizing a photoetching vector imaging model; the objective function D is constructed as the average value of the imaging fidelity function of each field point of the lithography objective, i.e.
Figure GDA0001760155540000066
Referring to the prior art (CN 102269926B, 2012.08.15), under the condition of considering the polarization aberration of the lithography system, the abbe vector imaging model is used to calculate the aerial image corresponding to the current light source and the mask as:
Figure GDA0001760155540000067
wherein the content of the first and second substances,
Figure GDA0001760155540000068
and | | represents the modulo of each element in the matrix, and the final calculation result I is a scalar matrix (if all elements in a matrix are scalars, the matrix is called a scalar matrix) with the size of N × N, and represents the intensity distribution of the aerial image corresponding to the current light source and the mask.
Figure GDA0001760155540000069
Is light source point J (x)s,ys) The corresponding mask diffraction matrix, defined as each point on the mask to light source point J (x) according to the Hopkins approximations,ys) The optical path length of (a):
Figure GDA00017601555400000610
where NA denotes the object-side numerical aperture of the projection system and pixel denotes the side length of the individual sub-regions on the mask pattern.
Figure GDA0001760155540000071
Representing a convolution, ⊙ representing the direct multiplication of the corresponding elements of the two matrices,
Figure GDA0001760155540000072
representing the inverse Fourier transform, nwThe refractive index of the immersion liquid on the image side of the lithography system is shown, and R is the reduction magnification of an ideal projection system and is generally 4; v'pComprising vector matrices (if an element in a matrix is a vector or a matrix, it is called a vector matrix)
Figure GDA0001760155540000073
P-component composition of each element in (a); here, p represents the polarization direction of light, and represents the vector characteristic of the imaging model, and PA represents the polarization aberration of the lithography system. According to the polarization theory of light, PA is typically a 2 × 2 complex matrix (jones matrix). The specific calculation process of V' is described in detail in the prior art (CN 102269926B, 2012.08.15), and is not described herein again.
Sigmoid functions are used to approximately describe the lithographic effect,
Figure GDA0001760155540000074
where a represents the slope of the resist approximation model, trRepresenting the threshold of the resist approximation model. Therefore, the image in the photoresist corresponding to the light source pattern and the mask pattern is calculated according to the aerial image intensity I as:
Figure GDA0001760155540000075
according to the calculation process, the polarization aberration PA corresponding to each view field point is comprehensively considerediAnd calculating to obtain an imaging fidelity function of each field of view point, and then taking the arithmetic mean to obtain a specific numerical value of the target function D.
(4) Comprehensively considering the polarization aberration PA corresponding to each view field pointiUnder the condition, the objective function D is calculated to be corresponding to the light source variable matrix omegasGradient matrix of
Figure GDA0001760155540000076
Summing the pixel values J of each pixel point on the light source graphsumApproximating to a given constant to obtain an approximation of the gradient matrix
Figure GDA0001760155540000077
Calculating the objective function D versus the mask variable matrix omegaMGradient matrix of
Figure GDA0001760155540000078
Gradient matrix
Figure GDA0001760155540000079
For the objective function D to the variable matrix omegaMThe partial derivative of each element in the series is obtained.
The polarization aberration considered in the present invention is derived from factors such as scattering on the lens surface, film layer and crystal birefringence effects. The polarization aberration data used in the present invention can be obtained by the CODEC software tracing the multiple refraction and reflection of light in the projection objective. In a specific application, the polarization aberration data of the lithography objective can also be obtained through actual measurement.
According to the step (3), the gradient matrix
Figure GDA0001760155540000081
Gradient matrix
Figure GDA0001760155540000082
Reference (J.Opt.Soc.Am.A., 2013, 30: 112-
Figure GDA0001760155540000083
And
Figure GDA0001760155540000084
the specific form of (1):
Figure GDA0001760155540000085
Figure GDA0001760155540000086
wherein, tableThe conjugate operation is taken, and the matrix is rotated by 180 degrees in both the transverse and longitudinal directions. Calculating point correspondence of different fields of view
Figure GDA0001760155540000087
And
Figure GDA0001760155540000088
when it is needed only at
Figure GDA0001760155540000089
Different polarization aberration data are introduced.
Updating the light source variable matrix omega by using the steepest descent methodsIs composed of
Figure GDA00017601555400000810
Obtaining a corresponding current omegasThe light source pattern J of (a),
Figure GDA00017601555400000811
updating mask variable matrix omega by using steepest descent methodMIs composed of
Figure GDA00017601555400000812
Wherein
Figure GDA00017601555400000813
Obtaining the corresponding current omega for the preset mask optimization step lengthMThe mask pattern M of (a) is,
Figure GDA00017601555400000814
updating binary mask pattern M corresponding to current Mb，
Figure GDA00017601555400000815
In general tmTake 0.5.
(5) Calculating the current light source pattern J and the binary mask pattern MbThe value of the corresponding objective function D; when the value is less than the predetermined threshold value delta D or the light source variable matrix omega is updatedsAnd mask variable matrix omegaMReaches a predetermined upper limit value KSMWhen the temperature of the water is higher than the set temperature,and (6) is entered, otherwise, the step (4) is returned.
(6) Terminating the optimization, and combining the current light source pattern J and the binary mask pattern MbAnd determining the optimized light source pattern and mask pattern.
Example of implementation of the invention:
as shown in fig. 3, which is a schematic diagram of the position of the field point of the lithography objective, the polarization aberration corresponding to each field point is obtained by performing ray tracing through the optical design software CODEV. In general, the edge field point F11 has the largest polarization aberration value and the central field point F3 has the smallest polarization aberration value.
FIG. 4 is a schematic diagram of an initial light source, an initial mask and its corresponding imaging in photoresist. In fig. 4, 401 is an initial light source pattern, white represents a light-emitting portion, and black represents a non-light-emitting portion. 402 is the initial mask pattern and also the target pattern, white represents the light-transmitting area and black represents the light-blocking area, with a feature size of 45 nm.
Fig. 5 is a schematic diagram of a light source pattern and a mask pattern optimized by a related art (CN 102269926B, 2012.08.15) (hereinafter, abbreviated as method a) for polarization aberration corresponding to the extreme field point F11. In fig. 5, 501 is a light source pattern optimized by the method a; 502 is the mask pattern optimized using method a.
Fig. 6 shows a schematic diagram of a light source pattern and a mask pattern after optimization by the multi-objective light source-mask optimization method (hereinafter abbreviated as method B) in accordance with the present invention for full-field polarization aberration (due to symmetry, polarization aberrations corresponding to 9 field points in total of F1-F3, F6-F8, and F11-F13 are considered here). In fig. 6, 601 is a light source pattern optimized by the method a; 602 is the mask pattern optimized using method a.
Patterning errors, which are used herein to describe lithographic imaging quality, can be considered to be approximately equal to imaging fidelity under a hard threshold photoresist model. Table 1 gives the graphic error data for method a and method B imaged at different field points:
TABLE 1 graphic error data corresponding to different methods at each view point
Figure GDA0001760155540000091
Figure GDA0001760155540000101
The data in Table 1 show that for method A, lithographic imaging quality was higher at the extreme field of view point F11 and less effective lithographic imaging was achieved at the central field of view point F3. This is because the method a is optimized only for the polarization aberration corresponding to F11, and the optimization result is only suitable for F11 and its close field point, not for F3 field point far from F11. For method B, since the polarization aberration information of 9 field points is considered in the optimization process, it is suitable for full-field lithography imaging, i.e. the pattern errors imaged at each field point are relatively averaged. Further, it can be calculated from the data in table 1, the mean value of the pattern errors of the method a imaging at 9 field points is 690, the standard deviation is 103, and the PV value is 263; method B imaged pattern error at 9 field points with an average value of 822, standard deviation of 195, and PV value of 503. The data comparison shows that compared with the existing method A, the imaging quality of the method B provided by the invention in the full-field range is more uniform (standard deviation and PV value are both reduced), the whole pattern error is also reduced, the improvement of the yield of the photoetching process is facilitated, and the superiority of the method is reflected.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it will be understood by those skilled in the art that various changes, substitutions and alterations can be made herein without departing from the principles of the invention, and these should be considered as falling within the scope of the invention.

Claims (2)

1. The multi-target light source and mask optimization method for improving the full-field photoetching imaging uniformity is characterized by comprising the following steps of:
step one, initializing a light source pattern and a mask pattern, and specifically comprising:
step 101, initializing a light source to a size of NS×NSLight source diagram ofShape J, initializing mask pattern M to target pattern of size N
Figure FDA0002359223360000011
Wherein N isSAnd N is an integer;
102, setting the pixel value of a light-emitting area on the initial light source graph J to be 1 and the pixel value of a non-light-emitting area to be 0; set size to NS×NSLight source variable matrix omegas: when J (x)s,ys) When the number is equal to 1, the alloy is put into a container,
Figure FDA0002359223360000012
when J (x)s,ys) When the content is equal to 0, the content,
Figure FDA0002359223360000013
wherein J (x)s,ys) Representing a pixel point (x) on the light source patterns,ys) A pixel value of (a); setting the transmissivity of a light transmission area of the initial mask pattern M to be 1 and the transmissivity of a light blocking area to be 0; setting a mask variable matrix Ω of size N × NM: when M (x, y) is 1,
Figure FDA0002359223360000014
when M (x, y) is 0,
Figure FDA0002359223360000015
wherein M (x, y) represents the transmittance of each pixel (x, y) on the mask pattern; let the initial mask pattern Mb＝M；
Step two, constructing an optimized objective function D:
polarization aberration PA based on lithography objective ith view field point correspondenceiDetermining an imaging fidelity function for an ith field of view point
Figure FDA0002359223360000016
Wherein i is 1,2, n, n is the number of field points;
Figure FDA0002359223360000017
the pixel value of each pixel point of the target graph is taken; z (x, y, PA)i) Presentation taking into account polarization aberrations PAiUnder the condition of (1), calculating the pixel value of each pixel point in the photoresist imaging corresponding to the current light source pattern and the mask pattern by utilizing a photoetching imaging model; the objective function D is constructed as the average value of the imaging fidelity function of each field point of the lithography objective, i.e.
Figure FDA0002359223360000018
Thirdly, optimizing a light source and a mask based on the optimized objective function D, and specifically comprising the following steps:
step 301, calculating a light source variable matrix omega of the objective function D corresponding to the current light source graphsGradient matrix ▽ D (Ω)s) Adding the pixel values of each pixel point on the light source graph to obtain a sum JsumApproximating to a given constant, and then obtaining an approximation of the gradient matrix
Figure FDA0002359223360000021
Calculating a mask variable matrix omega corresponding to the target function D to the current mask patternMGradient matrix ▽ D (Ω)M) (ii) a Updating the light source variable matrix omega by using the steepest descent methodsIs composed of
Figure FDA0002359223360000022
Obtaining a corresponding current omegasLight source pattern J of (a):
Figure FDA0002359223360000023
updating mask variable matrix omega by using steepest descent methodMIs composed of
Figure FDA0002359223360000024
Wherein
Figure FDA0002359223360000025
Obtaining the corresponding current omega for the preset mask optimization step lengthMIs masked withForm M:
Figure FDA0002359223360000026
updating a binary mask pattern M corresponding to a current mask pattern Mb：
Figure FDA0002359223360000027
tmTaking the value as 0.5; wherein, J (x)s,ys) Representing each pixel point (x) on the light source pattern Js,ys) A pixel value of (a); m (x, y) represents the transmittance of each pixel point (x, y) on the mask pattern;
step 302, calculating the current light source pattern J and the binary mask pattern MbThe value of the corresponding objective function D; when the value is less than the predetermined threshold value or the light source variable matrix omega is updatedsAnd mask variable matrix omegaMWhen the number of times reaches a preset upper limit value, the step 303 is entered, otherwise, the step 301 is returned to;
step 303, terminating the optimization, and combining the current light source pattern J and the mask pattern MbAnd determining the optimized light source pattern and mask pattern.
2. The method of claim 1, wherein the polarization aberration PA is a multi-objective light source and mask optimization to improve full field lithographic imaging uniformityiCalculated under the premise of considering the influence of lens surface scattering and film and crystal birefringence effects.
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