CN110262191B - Computational lithography modeling method and device - Google Patents
Computational lithography modeling method and device Download PDFInfo
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- CN110262191B CN110262191B CN201910385455.2A CN201910385455A CN110262191B CN 110262191 B CN110262191 B CN 110262191B CN 201910385455 A CN201910385455 A CN 201910385455A CN 110262191 B CN110262191 B CN 110262191B
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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
- G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
- G03F7/70—Microphotolithographic exposure; Apparatus therefor
- G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
- G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
- G03F7/705—Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions
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- G06F30/39—Circuit design at the physical level
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Abstract
The application relates to the technical field of integrated circuit manufacturing, and discloses a computational lithography modeling method and a computational lithography modeling device. And calculating ideal light intensity distribution of the optical module group on the photoresist, and acquiring parameters of the photochemical model according to the ideal light intensity distribution and photochemical reaction excited by the optical module group on the photoresist. And then simulating the boundary position formed by the test pattern on the photoresist, acquiring key dimension simulation data of the test pattern, and establishing a computational lithography model if the fitting error between the key dimension measurement data and the key dimension simulation data is not greater than a preset allowable error. According to the computational lithography modeling method, different optical modules are built to simulate different graphic units, and the accuracy of the computational lithography model is effectively improved.
Description
Technical Field
The present application relates to the field of integrated circuit manufacturing technologies, and in particular, to a computational lithography modeling method and apparatus.
Background
With the development of the photolithography process, the size of the device in the integrated circuit manufacturing process is developed from submicron to ultra-deep submicron, i.e. the critical line width of the device is continuously reduced. As the critical line width of a device is reduced, the Optical Proximity Effect (OPE) in the photolithography process becomes more and more prominent, and OPE refers to a pattern which is pre-designed on a reticle due to the diffraction phenomenon of a photolithography system and various physicochemical effects, and after the pattern is transferred to the surface of a wafer, the obtained pattern generates various distortions, such as narrowing of line width and the like. To solve this problem, a model-based Optical Proximity Correction (OPC) technique is usually used to correct the reticle pattern before photolithography, so that the photolithography result can match the pre-designed result.
The key to the model-based OPC technology is to build an accurate computational lithography model. The computational lithography model comprises a physical optical model and a photochemical model, wherein the physical optical model is mainly a model established for the optical module, and the photochemical model is mainly a model established for a series of photochemical reactions generated on the photoresist. The two models can be described by a series of model parameters (including physical optical model parameters and photochemical model parameters), which need to be fitted by using measurement data, wherein the better the fitting result is, the higher the accuracy of calculating the photolithography model is, and the measurement data refers to the data obtained by transferring the pattern for testing, namely the test pattern, written on the mask plate onto the surface of the wafer and then measuring the line width of the pattern on the surface of the wafer. The process of building a computational lithography model can be said to correspond to the process of optimizing the model parameters. Therefore, in the process of establishing the computational lithography model, the test pattern needs to be continuously simulated based on the model parameters, the obtained simulation data is fitted with the measurement data, whether the parameters are optimized is judged by judging whether the fitting result meets the preset conditions, and then the accurate computational lithography model is established.
A test pattern is a collection of graphic elements having typical features, such as isolated lines (isoline), dense lines (dense), line ends (line end), and other specially designed graphic elements, and a test pattern is usually composed of thousands of the above graphic elements. In a set of calculation lithography model parameters, when a test pattern is simulated and fitted, the obtained fitting results are different for different pattern units according to physical optical model parameters corresponding to an optical module, and therefore, when the model parameters are optimized by using the fitting results, the accuracy of the optimized results cannot be ensured. Therefore, with the increasing complexity of the test patterns, the accuracy of the calculation of the lithography model cannot meet the requirements of the lithography process.
Disclosure of Invention
In order to improve the accuracy of the computational lithography model, the present application discloses a computational lithography modeling method and apparatus by the following embodiments.
In a first aspect of the present application, a computational lithography modeling method is disclosed, comprising:
obtaining the type of a graphic unit contained in a test pattern, wherein the test pattern refers to a mask pattern used for testing;
determining an optical module group according to the type of the graphic unit, wherein the optical module group consists of a plurality of optical modules;
acquiring parameters of a physical optical model according to the optical module group;
calculating ideal light intensity distribution of the optical module group on the photoresist according to the optical module group and the test pattern, wherein the ideal light intensity distribution comprises the ideal light intensity distribution of each optical module on the photoresist;
acquiring parameters of a photochemical model according to the ideal light intensity distribution and photochemical reactions excited by the optical module group on the photoresist;
obtaining a threshold condition of the photo-resist for photochemical reaction, and simulating a boundary position formed by the test pattern on the photo-resist according to the threshold condition and the ideal light intensity distribution;
obtaining key dimension measurement data of the test pattern, and obtaining key dimension simulation data of the test pattern according to the boundary position;
and if the fitting error between the critical dimension measurement data and the critical dimension simulation data is not larger than the preset allowable error, establishing a computational lithography model according to the parameters of the physical optical model and the parameters of the photochemical model, wherein the computational lithography model comprises the physical optical model and the photochemical model.
Optionally, if the fitting error is greater than the preset allowable error, the parameters of the physical optical model and the parameters of the photochemical model are obtained again according to a newton iteration method, and the computational lithography model is optimized.
Optionally, the determining an optical module group according to the type of the graphic unit includes:
classifying the test pattern according to the type of the pattern unit;
acquiring the proportion of each type of test pattern in the test patterns;
determining an optical module corresponding to each type of test pattern;
determining the weight coefficient of the optical module corresponding to each type of test pattern according to the proportion of each type of test pattern in the test pattern;
and combining the optical modules corresponding to each type of test pattern according to respective weight coefficients to determine the optical module group.
Optionally, the parameters of the physical optical model include optical parameters corresponding to each optical module;
wherein, the optical parameters corresponding to each optical module include: illumination source parameters, pupil lens parameters, and imaging depth parameters.
Optionally, the parameters of the photochemical model include parameters of photochemical reactions excited by each of the optical modules on the photoresist;
wherein the photochemical reaction parameters excited by each optical module on the photoresist comprise: the weight coefficient of the optical module, the weight coefficient of an ideal light intensity distribution diffusion term of the optical module, the standard deviation of a Gaussian function and the order of a Laguerre polynomial.
Alternatively to this, the first and second parts may,
calculating the boundary position by the following formula, wherein the boundary position is a coordinate set of a light resistance image formed on the photoresist by the optical module group based on the test pattern:
wherein i represents the ith optical module; c. CiA weight coefficient representing the ith optical module; ri(xk,yk) Representing a light blocking image formed on the photoresist by the ith optical module based on the test pattern; (x)k,yk) Coordinates representing a light blocking image formed on the photoresist by the i-th optical module based on the test pattern; t represents the threshold condition for the photo-resist to undergo a photochemical reaction.
Optionally, based on the test pattern, a photoresist image formed on the photoresist by the ith optical module is:
wherein j represents the jth diffusion term of the ideal light intensity distribution of the ith optical module,/jA weight coefficient, I, of a jth diffusion term representing an ideal light intensity distribution of the ith optical modulei(x, y) represents an ideal light intensity distribution of the ith optical module on the photoresist,
representing the laguerre basis function of Gauss, sjRepresenting the standard deviation, p, of said Gaussian functionjRepresenting the order of the laguerre polynomial.
Optionally, the fitting error is:
err＝∑|MeasureCD-SimulationCD|2；
where err represents the fitting error, MeasureCDRepresenting the critical dimension measurement data, SimulationCDRepresenting the critical dimension simulation data.
In a second aspect of the present application, there is disclosed a computational lithography modeling apparatus comprising:
the system comprises a graph acquisition module, a graph analysis module and a graph analysis module, wherein the graph acquisition module is used for acquiring the type of a graph unit contained in a test graph, and the test graph refers to a mask graph used for testing;
the optical module group determining module is used for determining an optical module group according to the type of the graphic unit, wherein the optical module group consists of a plurality of optical modules;
the physical optical model parameter acquisition module is used for acquiring parameters of the physical optical model according to the optical module group;
an ideal light intensity calculation module, configured to calculate an ideal light intensity distribution of the optical module group on the photoresist according to the optical module group and the test pattern, where the ideal light intensity distribution includes an ideal light intensity distribution of each of the optical modules on the photoresist;
the photochemical model parameter acquisition module is used for acquiring parameters of a photochemical model according to the ideal light intensity distribution and photochemical reaction excited by the optical module group on the photoresist;
the simulation module is used for acquiring a threshold condition of the photo-resist for photochemical reaction and simulating a boundary position formed by the test pattern on the photo-resist according to the threshold condition and the ideal light intensity distribution;
the data acquisition module is used for acquiring key dimension measurement data of the test pattern and acquiring key dimension simulation data of the test pattern according to the boundary position;
and the model establishing module is used for establishing a computational lithography model according to the parameters of the physical optical model and the parameters of the photochemical model when the fitting error between the critical dimension measurement data and the critical dimension simulation data is not more than a preset allowable error, wherein the computational lithography model comprises the physical optical model and the photochemical model.
Optionally, the apparatus further comprises:
and the optimization module is used for re-acquiring the parameters of the physical optical model and the parameters of the photochemical model according to a Newton iteration method and optimizing the computational lithography model when the fitting error is larger than the preset allowable error.
Optionally, the optical module group determining module includes:
the test pattern classification unit is used for classifying the test patterns according to the types of the pattern units;
the proportion obtaining unit is used for obtaining the proportion of each type of test pattern in the test patterns;
the optical module determining unit is used for determining the optical module corresponding to each type of test pattern;
the weight coefficient determining unit is used for determining the weight coefficient of the optical module corresponding to each type of test pattern according to the proportion of each type of test pattern in the test pattern;
and the optical module group determining unit is used for combining the optical modules corresponding to the test patterns according to respective weight coefficients to determine the optical module group.
Optionally, the parameters of the physical optical model include optical parameters corresponding to each optical module;
wherein, the optical parameters corresponding to each optical module include: illumination source parameters, pupil lens parameters, and imaging depth parameters.
Optionally, the parameters of the photochemical model include parameters of photochemical reactions excited by each of the optical modules on the photoresist;
wherein the photochemical reaction parameters excited by each optical module on the photoresist comprise: the weight coefficient of the optical module, the weight coefficient of an ideal light intensity distribution diffusion term of the optical module, the standard deviation of a Gaussian function and the order of a Laguerre polynomial.
Optionally, the simulation module is further configured to calculate the boundary position by using the following formula, where the boundary position is a coordinate set of a light blocking image formed on the photoresist by the optical module group based on the test pattern:
wherein i represents the ith optical module; c. CiA weight coefficient representing the ith optical module; ri(xk,yk) Representing a light blocking image formed on the photoresist by the ith optical module based on the test pattern; (x)k,yk) Coordinates representing a light blocking image formed on the photoresist by the i-th optical module based on the test pattern; t represents the threshold condition for the photo-resist to undergo a photochemical reaction.
Optionally, based on the test pattern, a photoresist image formed on the photoresist by the ith optical module is:
wherein j represents the jth diffusion term of the ideal light intensity distribution of the ith optical module,/jA weight coefficient, I, of a jth diffusion term representing an ideal light intensity distribution of the ith optical modulei(x, y) represents an ideal light intensity distribution of the ith optical module on the photoresist,
representing the laguerre basis function of Gauss, sjRepresenting the standard deviation, p, of said Gaussian functionjRepresenting the order of the laguerre polynomial.
Optionally, the fitting error is:
err＝∑|MeasureCD-SimulationCD|2；
where err represents the fitting error, MeasureCDRepresenting the critical dimension measurement data, SimulationCDRepresenting the critical dimension simulation data.
In the method, an optical module group is determined by obtaining the type of a graph unit contained in a test graph, and then parameters of a physical optical model are obtained according to the optical module group. And then calculating ideal light intensity distribution of the optical module group on the photoresist, and acquiring parameters of the photochemical model according to the ideal light intensity distribution and photochemical reaction excited by the optical module group on the photoresist. And then simulating the boundary position formed by the test pattern on the photoresist, acquiring key dimension simulation data of the test pattern, and establishing a computational lithography model if the fitting error between the key dimension measurement data and the key dimension simulation data is not greater than a preset allowable error. The computational lithography modeling method disclosed by the application aims at different graphic units in a test graph, and by establishing different optical modules for simulation and fitting, the precision of the computational lithography model is effectively improved, and under the condition of higher complexity of the test graph, the precision of the computational lithography model can be ensured to meet the requirements of the lithography process.
Drawings
In order to more clearly explain the technical solution of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious to those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic workflow diagram of a computational lithography modeling method according to an embodiment of the present disclosure;
FIG. 2 is a schematic flowchart illustrating a process of determining an optical module group in a computational lithography modeling method according to an embodiment of the present application;
FIG. 3A is a schematic diagram of a graph unit included in a first type of test pattern in a computational lithography modeling method according to an embodiment of the present disclosure;
FIG. 3B is a schematic diagram of a graph unit included in a second type of test pattern in the computational lithography modeling method according to the embodiment of the present disclosure;
fig. 3C is a schematic diagram of a graph unit included in a third type of test pattern in the computational lithography modeling method according to the embodiment of the present application;
FIG. 3D is a schematic diagram of a graph unit included in other types of test patterns in a computational lithography modeling method according to an embodiment of the present disclosure;
FIG. 4 is a schematic diagram of light source types in a computational lithography modeling method according to an embodiment of the present disclosure;
FIG. 5 is a schematic structural diagram of a physical optical model in a computational lithography modeling method according to an embodiment of the present application;
FIG. 6 is a schematic structural diagram of a photoresist imaging depth in a computational lithography modeling method according to an embodiment of the present application;
FIG. 7 is a schematic diagram of critical dimension simulation data in a computational lithography modeling method according to an embodiment of the present application;
FIG. 8 is a schematic diagram of a workflow for determining whether to optimize a model in a computational lithography modeling method disclosed in an embodiment of the present application;
FIG. 9 is a schematic workflow diagram of another computational lithography modeling method disclosed in an embodiment of the present application;
FIG. 10 is a diagram illustrating the results of a plurality of light sources illuminating a photoresist image formed in a computational lithography modeling method according to an embodiment of the present disclosure;
FIG. 11 is a schematic structural diagram of a computational lithography modeling apparatus according to an embodiment of the present disclosure.
Detailed Description
In order to improve the accuracy of the computational lithography model, the present application discloses a computational lithography modeling method and apparatus by the following embodiments.
The first embodiment of the present application discloses a computational lithography modeling method, referring to a workflow diagram shown in fig. 1, the method including:
step S110, obtaining the type of a graphic unit contained in a test pattern, wherein the test pattern refers to a mask pattern for testing.
Step S120, determining an optical module group according to the type of the graphic unit, wherein the optical module group is composed of a plurality of optical modules.
Referring to fig. 2, fig. 2 is a schematic flowchart illustrating a workflow for determining an optical module group according to the type of the graphics unit, disclosed in an embodiment of the present application, including:
and step S1201, classifying the test pattern according to the type of the pattern unit.
In actual production, a reticle pattern for testing typically contains thousands of pattern units. In the embodiment of the application, the test patterns are roughly divided into a first type test pattern, a second type test pattern, a third type test pattern and other types of test patterns according to the types of the graphic units. The first type of test graphics comprises several graphics units, namely, isoline, inv _ isoline, double and dense, the second type of test graphics comprises several graphics units, namely, line _ end, inv _ line _ end and dense _ line _ end, the third type of test graphics comprises a graphics unit, namely, dense _ contact, and the other types of test graphics are a collection of some special graphics units, such as, for example, Iso _ pad _ single, break _ H, line _ end _ drained and the like. Referring to fig. 3A to fig. 3D, fig. 3A schematically illustrates a graphic element included in a first type of test pattern, fig. 3B schematically illustrates a graphic element included in a second type of test pattern, fig. 3C schematically illustrates a graphic element included in a third type of test pattern, and fig. 3D schematically illustrates a graphic element included in another type of test pattern.
Step S1202, the proportion of each type of test pattern in the test patterns is obtained.
Step S1203, determining an optical module corresponding to each type of test pattern.
In one implementation, the test patterns are classified by obtaining the types of the pattern units included in the test patterns, and then the corresponding optical modules are determined to form the optical module group of the physical optical model. When determining the optical module, any light source with the best simulation effect for a certain type of test pattern in practical application can be used as the corresponding optical module. Specifically, a first optical module is determined aiming at a first type of test pattern; determining a second optical module aiming at the second type of test pattern; determining a third optical module aiming at the third type of test pattern; and determining the Nth optical module aiming at other types of test patterns. The number of optical modules is determined according to the number of test pattern classes in practical application.
In actual process production, an optical module is usually formed by using a coherent light source, and common coherent light sources include, but are not limited to, the following: a ring light source, a dipole light source, a quadrupole symmetric light source and a quadrupole asymmetric light source, and fig. 4 exemplarily shows a schematic diagram of the ring light source, the dipole light source and the quadrupole asymmetric light source. A quadrupole symmetric light source is of the same type as a bipolar light source except that the bipolar light source has two sectors and the quadrupole symmetric light source has 4 sectors.
Step S1204, determining the weight coefficient of the optical module corresponding to each type of test pattern according to the proportion of each type of test pattern in the test pattern.
According to the proportion of each type of test pattern in the whole test pattern, the importance degree of each type of test pattern to the whole test pattern can be obtained, and then the weight coefficient of the optical module corresponding to each type of test pattern can be determined according to the importance degree.
And step S1205, combining the optical modules corresponding to each type of test pattern according to respective weight coefficients to determine the optical module group.
The computational lithography modeling method disclosed by the embodiment of the application classifies the test patterns based on different types of graphic units, further determines a plurality of optical modules, and constructs an optical module group, so that the finally established computational lithography model can have a good fitting effect on different types of graphic units.
Step S130, obtaining parameters of the physical optical model according to the optical module group.
Referring to fig. 5, in the computational lithography model, a typical physical optical model is mainly composed of several components, i.e., a light source, a reticle, a pupil lens and an imaging plane. In conjunction with the physical optical model, the process of the lithography process can be summarized by the following flow: the light source passes through an opening on the mask plate and a group of pupil lenses to form certain optical intensity distribution on an imaging plane, wherein the optical intensity distribution is referred to as light intensity distribution for short.
In the embodiment of the present application, an optical system in the physical optical model is constituted by a plurality of light sources, i.e., a plurality of optical modules. Since the optical module group is composed of a plurality of optical modules, correspondingly, the parameters of the physical optical model include the optical parameters corresponding to each optical module, that is, the parameters of the physical optical model need to be obtained for each optical module. The optical parameters corresponding to each optical module include: illumination source parameters, pupil lens parameters, and imaging depth parameters.
The parameters of the illumination source include the inner diameter σ of the sourceinOuter diameter of light source sigmaoutAnd the angles phi and psi of the sector light sources, etc., are labeled in fig. 4 for the parameters related to the inner diameter of the light source, the outer diameter of the light source, and the angle of the light source on different light sources, in conjunction with the light source schematic diagram shown in fig. 4.
The pupil lens parameters include the phase difference W (f, g) of the lens, which is usually expressed as a Zeinike polynomial, defocus Δ z, and the like.
The imaging depth parameter is a certain imaging depth idepth of the optical module on the photoresist. In the embodiment of the present application, the obtained measurement data of the critical dimension of the test pattern, which is disclosed later, is the measurement result on the boundary of the photoresist because the photoresist on the imaging plane has a certain thickness, see the schematic diagram of the imaging depth of the photoresist given in fig. 6, the plane of the x-y direction refers to the plane of the imaging depth, the z direction refers to the direction perpendicular to the plane of the test pattern, and the arrow of the "Measure CD" refers to the measurement result of the critical dimension at a certain imaging depth. It can be seen that there is a certain slope in the z-direction of the critical dimension measurement. The slope is significantly different for different test patterns. Therefore, in order to better fit the measured data, in the embodiment of the present application, the imaging depth is taken as one of the optical parameters of the optical module, and the subsequently disclosed critical dimension simulation data is a calculation result of a certain imaging depth of the optical module group on the photoresist.
It should be noted that the optical parameters of the optical module include, but are not limited to, the several parameters disclosed above, and the optical parameters may be adaptively added or deleted according to the requirements of the practical application. The parameters of the physical optical model disclosed in the embodiments of the present application can be uniformly described as follows:
where i denotes the ith optical module and "…" denotes the optical parameter, which is not limited to these. Specifically, in combination with the four light sources disclosed above, the embodiments of the present application respectively disclose parameters of a physical optical modelNumber, wherein for a ring light source, the physical optical model parameters can be described as:
for a bi-polar light source, the optical parameters can be described as:
for a quadrupole asymmetric light source, the optical parameters can be described as:
for a quadrupole symmetric light source, the optical parameters can be described as:
step S140, calculating ideal light intensity distribution of the optical module group on the photoresist according to the optical module group and the test pattern, wherein the ideal light intensity distribution comprises the ideal light intensity distribution of each optical module on the photoresist.
According to the existing calculation lithography principle, based on the Hopkins diffraction optical theory, the ideal light intensity distribution of an optical module on the photoresist can be calculated by the following formula:
Ii(x,y)＝∫∫TCCi(x-x1,y-y1；x-x2,y-y2)M(x1,y1)M*(x2,y2)dx1dx2dy1dy2。
wherein, Ii(x, y) represents an ideal light intensity distribution of the ith optical module on the photoresist, M () represents a test pattern function, M*() Is the complex conjugate of M (), TCCi() The cross transfer function corresponding to the ith optical module is a four-dimensional convolution function operation of a light source function and a pupil function, is used for describing and calculating the optical transmission property in the photoetching model, and can be expressed by the following formula:
TCCi(x1,y1；x2,y2)＝s(x1-x2,y1-y2)p(x1,y1)p*(x2,y2)。
where s () is the light source function describing the coherence properties of the illumination source, p () is the pupil lens function, p*() Is the complex conjugate of p ().
In the above formula of the cross transfer function, the light source function is a function in a spatial domain, and can be obtained by performing inverse fourier transform on the function in a frequency domain, specifically expressed as: s (x, y) ═ F-1[S(f,g)]Where s (x, y) is a function of the light source in the spatial domain, F-1[]Expressing the inverse Fourier transform, S (f, g) is a light source function on a frequency domain, x, y) expresses the coordinate position of the light source on a space domain, and f, g expresses the coordinate position of the light source on the frequency domain. In the embodiment of the present application, in combination with the ring light source disclosed above, the light source function of the ring light source is given as follows:
it should be noted that, corresponding to the 4 light sources disclosed above, in the embodiment of the present application, there are four different cross transfer functions.
And S150, acquiring parameters of a photochemical model according to the ideal light intensity distribution and photochemical reactions excited by the optical module group on the photoresist.
For a certain optical module in the physical optical model, the optical module is projected on the photoresist, excited by photochemical reaction, baked and developed to form a photoresist pattern. The developed cross-sectional view of the resist pattern is simulated by chemical reaction on the resist, and is referred to as a resist image. When the optical module projects on the photoresist, the ideal light intensity distribution has diffusion, the diffusion term of the ideal light intensity distribution can be described through the convolution of the Gaussian Laguerre basis function and the ideal light intensity distribution function, and the photoresist image is equivalent to the summation of all the diffusion terms of the ideal light intensity distribution.
The pattern formed on the photoresist is the result of the cooperation of the plurality of optical modules. Therefore, in the embodiment of the present application, the parameters of the photochemical model include parameters of photochemical reactions excited on the photoresist by each of the optical modules. Wherein the photochemical reaction parameters excited by each optical module on the photoresist comprise: the weight coefficient of the optical module, the weight coefficient of an ideal light intensity distribution diffusion term of the optical module, the standard deviation of a Gaussian function and the order of a Laguerre polynomial.
It should be noted that the photochemical reaction parameters include, but are not limited to, the several parameters disclosed above, and may be adaptively added or deleted according to the needs of the practical application. The parameters of the photochemical model disclosed in the embodiments of the present application can be described uniformly as: { ci,sj,pj,lj…, where i denotes the ith optical module, j denotes the jth diffusion term of the ideal intensity distribution of the ith optical module, ciRepresents the weight coefficient, s, of the ith optical modulejRepresenting the standard deviation, p, of a Gaussian functionjOrder of the laguerre polynomial, ljThe weight coefficient of the jth diffusion term in the ideal light intensity distribution of the ith optical module is shown, and the expression "…" indicates that the photochemical reaction parameter is not limited to these parameters.
Step S160, obtaining a threshold condition of the photo-resist for photochemical reaction, and simulating a boundary position formed by the test pattern on the photo-resist according to the threshold condition and the ideal light intensity distribution.
The threshold condition refers to a threshold condition of photoresist exposure, that is, a density value of a minimum energy required for a light source to form a pattern on the photoresist, and the threshold condition can be obtained according to characteristics and kinds of the photoresist in practical applications.
In this embodiment of the present application, the boundary position formed on the photoresist can be calculated by the following formula, where the boundary position is a coordinate set of a photoresist image formed on the photoresist by the optical module group based on the test pattern:
wherein i represents the ith optical module; c. CiA weight coefficient representing the ith optical module; ri(xk,yk) Representing a light blocking image formed on the photoresist by the ith optical module based on the test pattern; t represents a threshold condition for the photo-resist to generate photochemical reaction; (x)k,yk) Coordinates representing a resist image formed on the photoresist by the i-th optical module based on the test pattern, (x)k,yk) The set of coordinates constitutes the boundary position on the photoresist.
Based on the test pattern, the light resistance image formed on the photoresist by the ith optical module is as follows:
wherein R isi() A light blocking image representing the ith optical module, j represents the jth diffusion term of the ideal light intensity distribution of the ith optical module, ljA weight coefficient, I, of a jth diffusion term representing an ideal light intensity distribution of the ith optical modulei(x, y) represents an ideal light intensity distribution of the ith optical module on the photoresist,
representing the laguerre basis function of Gauss, sjRepresenting the standard deviation, p, of said Gaussian functionjRepresenting the order of the laguerre polynomial.
The expression of the gaussian laguerre basis function is:
step S170, obtaining the critical dimension measurement data of the test pattern, and obtaining the critical dimension simulation data of the test pattern according to the boundary position.
The critical dimension measurement data is data obtained by transferring a test pattern onto the surface of a wafer and measuring the line width of the pattern on the surface of the wafer. For the operation of obtaining the critical dimension measurement data of the test pattern, it is understood by referring to fig. 3A to 3D that the position of the critical dimension of each type of test pattern is exemplarily given by an arrow where "Measure CD" or "Measure CDs" is located, and the critical dimension measurement data of the test pattern can be obtained by measuring the critical dimension.
The boundary position is (x)k,yk) And acquiring the critical dimension simulation data of the test pattern according to the boundary position by the set of coordinates through the following formula:
SimulationCD＝|xk-xk-1|。
referring to fig. 7, a diagram of critical dimension Simulation data is shown, in which a curve represents a photoresist image, a rectangle represents a test pattern, an arrow with "Simulation CD" represents critical dimension Simulation data of the test pattern under the threshold condition T, and an arrow with "Measure CD" represents critical dimension measurement data of the test pattern.
In one implementation, after obtaining the critical dimension measurement data and the critical dimension simulation data of the test pattern, a fitting error between the critical dimension measurement data and the critical dimension simulation data needs to be calculated, in this embodiment, the fitting error is calculated by the following formula:
err＝∑|MeasureCD-SimulationCD|2。
where err represents the fitting error, MeasureCDRepresenting the critical dimension measurement data, SimulationCDRepresenting the critical dimension simulation data.
After the fitting error is obtained, it is necessary to determine whether the fitting error is not greater than a preset allowable error. In an implementation manner, referring to the workflow diagram shown in fig. 8, after step S170 is executed, the computational lithography modeling method disclosed in the embodiment of the present application further includes: step S210, determining whether a fitting error between the critical dimension measurement data and the critical dimension simulation data is not greater than a preset allowable error. If yes, executing step S180; if the determination result is no, step S211 is executed. The allowable error is a preset value, the size of the allowable error is set by a user according to the requirements of practical application, in the embodiment of the present application, the allowable error is set to tol-1 e-10, and "1 e-10" is a scientific counting method, and the size of the scientific counting method is expressed as minus ten times of ten.
Step S180, if the fitting error between the critical dimension measurement data and the critical dimension simulation data is not greater than a preset allowable error, establishing a computational lithography model according to the parameters of the physical optical model and the parameters of the photochemical model, where the computational lithography model includes the physical optical model and the photochemical model.
Step S211, if the fitting error is greater than the preset allowable error, re-obtaining the parameters of the physical optical model and the parameters of the photochemical model according to a newton iteration method, and optimizing the computational lithography model.
Newton's iteration method is a commonly used parameter optimization method. And under the condition that the fitting error is larger than the preset allowable error, the Newton iteration method is used for guiding the change of the parameters of the physical optical model and the parameters of the photochemical model, so that the optimization improvement of the computational lithography model is realized, and the finally obtained computational lithography model meets the process requirements.
The application discloses a computational lithography modeling method, in the method, an optical module group is determined by obtaining the type of a graph unit contained in a test graph, and then parameters of a physical optical model are obtained according to the optical module group. And calculating ideal light intensity distribution of the optical module group on the photoresist, and acquiring parameters of the photochemical model according to the ideal light intensity distribution and photochemical reaction excited by the optical module group on the photoresist. And then simulating the boundary position formed by the test pattern on the photoresist, acquiring key dimension simulation data of the test pattern, and establishing a computational lithography model if the fitting error between the key dimension measurement data and the key dimension simulation data is not greater than a preset allowable error. The computational lithography modeling method disclosed by the application aims at different graphic units in a test graph, and by establishing different optical modules for simulation and fitting, the precision of the computational lithography model is effectively improved, and under the condition of higher complexity of the test graph, the precision of the computational lithography model can be ensured to meet the requirements of the lithography process.
For further explanation of the present application, a computational lithography modeling method disclosed in the present application is described below with reference to examples, but they should not be construed as limiting the scope of the present application.
Referring to a workflow diagram shown in fig. 9, a computational lithography modeling method disclosed in an embodiment of the present application includes: firstly, reading in a test pattern, determining an optical module group by classifying the test pattern, and acquiring optical parameters of the optical module group, namely acquiring physical optical model parameters, specifically including acquiring a first optical module parameter, acquiring a second optical module parameter, …, acquiring an nth optical module parameter, and acquiring a cross transfer function of a corresponding optical module. And then, calculating the light intensity distribution corresponding to each optical module by combining the pattern function of the test mask, namely the test pattern function, specifically comprising calculating a first light intensity distribution, calculating a second light intensity distribution, … and calculating an Nth light intensity distribution. Then, determining the photochemical reaction parameters corresponding to each optical module according to the photochemical reaction excited by each optical module on the photoresist, namely acquiring the photochemical model parameters, specifically including acquiring the first photochemical reaction parameter, acquiring the second photochemical reaction parameter, …, and acquiring the nth photochemical reaction parameter. Then, the boundary position of the test pattern formed on the photoresist is simulated by calculating the photoresist image formed on the photoresist by each optical module. And then, acquiring critical dimension simulation data according to the boundary position, and calculating a fitting error between the critical dimension measurement data and the critical dimension simulation data. And finally, judging whether the calculation photoetching model is optimized or not by judging whether the fitting error is not larger than a preset allowable error or not. If the fitting error is not greater than the tolerance error, the accuracy of the current computational lithography model meets the requirement, and the previously acquired physical optical model parameters and photochemical model parameters can be determined as the computational lithography model parameters, so that the computational lithography model is established; and if the fitting error is larger than the tolerance error, the current calculation photoetching model precision does not meet the requirement, at the moment, the calculation photoetching model parameters need to be optimized, and the physical optical model parameters and the photochemical model parameters are obtained again according to a Newton iteration method.
According to the computational lithography modeling method disclosed by the embodiment of the application, the test patterns are classified according to different pattern units in the test patterns, and the test patterns are simulated and fitted by establishing different optical modules, so that the precision of the computational lithography model is effectively improved. Referring to fig. 10, the difference of the light blocking image finally formed by the test pattern is disclosed for the optical module group composed of 1 light source (one source), 2 light sources (two sources), 3 light sources (three sources) and 4 light sources (four sources), respectively. Those skilled in the art can easily verify the beneficial effects of the present application based on the disclosure of the above embodiments.
The following are embodiments of the apparatus of the present application that may be used to perform embodiments of the method of the present application. For details which are not disclosed in the embodiments of the apparatus of the present application, reference is made to the embodiments of the method of the present application.
The second embodiment of the present application discloses a computational lithography modeling apparatus, referring to a schematic structural diagram shown in fig. 11, the apparatus including:
the pattern acquisition module 10 is configured to acquire types of pattern units included in a test pattern, where the test pattern refers to a reticle pattern used for testing.
An optical module group determining module 20, configured to determine an optical module group according to the type of the graphics unit, where the optical module group is composed of a plurality of optical modules.
And the physical optical model parameter obtaining module 30 is configured to obtain parameters of the physical optical model according to the optical module group.
And the ideal light intensity calculation module 40 is configured to calculate an ideal light intensity distribution of the optical module group on the photoresist according to the optical module group and the test pattern, where the ideal light intensity distribution includes an ideal light intensity distribution of each of the optical modules on the photoresist.
And the photochemical model parameter acquisition module 50 is configured to acquire parameters of the photochemical model according to the ideal light intensity distribution and the photochemical reaction excited by the optical module group on the photoresist.
And the simulation module 60 is configured to obtain a threshold condition of the photo-resist undergoing a photochemical reaction, and simulate a boundary position formed by the test pattern on the photo-resist according to the threshold condition and the ideal light intensity distribution.
A data obtaining module 70, configured to obtain the critical dimension measurement data of the test pattern, and obtain the critical dimension simulation data of the test pattern according to the boundary position.
A model establishing module 80, configured to establish a computational lithography model according to the parameters of the physical optical model and the parameters of the photochemical model when a fitting error between the critical dimension measurement data and the critical dimension simulation data is not greater than a preset allowable error, where the computational lithography model includes the physical optical model and the photochemical model.
Further, the apparatus further comprises:
and the optimization module is used for re-acquiring the parameters of the physical optical model and the parameters of the photochemical model according to a Newton iteration method and optimizing the computational lithography model when the fitting error is larger than the preset allowable error.
Further, the optical module group determination module includes:
and the test pattern classification unit is used for classifying the test patterns according to the types of the pattern units.
And the proportion acquiring unit is used for acquiring the proportion of each type of test pattern in the test patterns.
And the optical module determining unit is used for determining the optical module corresponding to each type of test pattern.
And the weight coefficient determining unit is used for determining the weight coefficient of the optical module corresponding to each type of test pattern according to the proportion of each type of test pattern in the test pattern.
And the optical module group determining unit is used for combining the optical modules corresponding to the test patterns according to respective weight coefficients to determine the optical module group.
Further, the parameters of the physical optical model include optical parameters corresponding to each of the optical modules.
Wherein, the optical parameters corresponding to each optical module include: illumination source parameters, pupil lens parameters, and imaging depth parameters.
Further, the parameters of the photochemical model include parameters of photochemical reactions excited on the photoresist by each of the optical modules.
Wherein the photochemical reaction parameters excited by each optical module on the photoresist comprise: the weight coefficient of the optical module, the weight coefficient of an ideal light intensity distribution diffusion term of the optical module, the standard deviation of a Gaussian function and the order of a Laguerre polynomial.
Further, the simulation module is further configured to calculate the boundary position by the following formula, where the boundary position is a coordinate set of a light blocking image formed on the photoresist by the optical module group based on the test pattern:
wherein i represents the ith optical module; c. CiA weight coefficient representing the ith optical module; ri(xk,yk) Indicating that the ith optical module is lithographically based on the test patternForming a photoresist image on the glue; (x)k,yk) Coordinates representing a light blocking image formed on the photoresist by the i-th optical module based on the test pattern; t represents the threshold condition for the photo-resist to undergo a photochemical reaction.
Further, based on the test pattern, the photoresist image formed on the photoresist by the ith optical module is:
wherein j represents the jth diffusion term of the ideal light intensity distribution of the ith optical module,/jA weight coefficient, I, of a jth diffusion term representing an ideal light intensity distribution of the ith optical modulei(x, y) represents an ideal light intensity distribution of the ith optical module on the photoresist,
representing the laguerre basis function of Gauss, SjRepresenting the standard deviation, P, of said Gaussian functionjRepresenting the order of the laguerre polynomial.
Further, the fitting error is:
err＝∑|MeasureCD-SimulationCD|2。
where err represents the fitting error, MeasureCDRepresenting the critical dimension measurement data, SimulationCDRepresenting the critical dimension simulation data.
In specific implementation, the present application further provides a computer storage medium, where the computer storage medium may store a program, and the program may include some or all of the steps in the embodiments provided in the present application when executed. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM) or a Random Access Memory (RAM).
In addition, the embodiment of the present application also provides a computer program product containing instructions, which when run on a computer, causes the computer to perform some or all of the steps of the method described in the above embodiment.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer product. The computer program product includes one or more computer instructions. When loaded and executed on a computer, cause the processes or functions described in accordance with the embodiments of the application to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another computer readable storage medium, for example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wire or wirelessly. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that incorporates one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid state disk), among others.
The present application has been described in detail with reference to specific embodiments and illustrative examples, but the description is not intended to limit the application. Those skilled in the art will appreciate that various equivalent substitutions, modifications or improvements may be made to the presently disclosed embodiments and implementations thereof without departing from the spirit and scope of the present disclosure, and these fall within the scope of the present disclosure. The protection scope of this application is subject to the appended claims.
Claims (9)
1. A computational lithography modeling method, the method comprising:
obtaining the type of a graphic unit contained in a test pattern, wherein the test pattern refers to a mask pattern used for testing;
determining an optical module group according to the type of the graphic unit, wherein the optical module group consists of a plurality of optical modules;
acquiring parameters of a physical optical model according to the optical module group;
calculating ideal light intensity distribution of the optical module group on the photoresist according to the optical module group and the test pattern, wherein the ideal light intensity distribution comprises the ideal light intensity distribution of each optical module on the photoresist;
acquiring parameters of a photochemical model according to the ideal light intensity distribution and photochemical reactions excited by the optical module group on the photoresist;
obtaining a threshold condition of the photo-resist for photochemical reaction, and simulating a boundary position formed by the test pattern on the photo-resist according to the threshold condition and the ideal light intensity distribution;
obtaining key dimension measurement data of the test pattern, and obtaining key dimension simulation data of the test pattern according to the boundary position;
if the fitting error between the critical dimension measurement data and the critical dimension simulation data is not larger than a preset allowable error, establishing a computational lithography model according to the parameters of the physical optical model and the parameters of the photochemical model, wherein the computational lithography model comprises the physical optical model and the photochemical model;
wherein determining a set of optical modules based on the type of the graphical unit comprises:
classifying the test pattern according to the type of the pattern unit;
acquiring the proportion of each type of test pattern in the test patterns;
determining an optical module corresponding to each type of test pattern;
determining the weight coefficient of the optical module corresponding to each type of test pattern according to the proportion of each type of test pattern in the test pattern;
and combining the optical modules corresponding to each type of test pattern according to respective weight coefficients to determine the optical module group.
2. The method of claim 1, wherein if the fitting error is larger than the preset tolerance, the parameters of the physical optical model and the parameters of the photochemical model are obtained again according to a newton iteration method, and the computational lithography model is optimized.
3. The method of claim 1, wherein the parameters of the physical optical model include optical parameters corresponding to each of the optical modules;
wherein, the optical parameters corresponding to each optical module include: illumination source parameters, pupil lens parameters, and imaging depth parameters.
4. The method of claim 1, wherein the parameters of the photochemical model include photochemical reaction parameters of each of the optical modules excited on the photoresist;
wherein the photochemical reaction parameters excited by each optical module on the photoresist comprise: the weight coefficient of the optical module, the weight coefficient of an ideal light intensity distribution diffusion term of the optical module, the standard deviation of a Gaussian function and the order of a Laguerre polynomial.
5. The method of claim 4,
calculating the boundary position by the following formula, wherein the boundary position is a coordinate set of a light resistance image formed on the photoresist by the optical module group based on the test pattern:
wherein i represents the ith optical module; c. CiA weight coefficient representing the ith optical module; ri(xk,yk) Representing a light blocking image formed on the photoresist by the ith optical module based on the test pattern; (x)k,yk) Coordinates representing a light blocking image formed on the photoresist by the i-th optical module based on the test pattern; t represents the threshold condition for the photo-resist to undergo a photochemical reaction.
6. The method of claim 5,
based on the test pattern, the light resistance image formed on the photoresist by the ith optical module is as follows:
wherein j represents the jth diffusion term of the ideal light intensity distribution of the ith optical module,/jA weight coefficient, I, of a jth diffusion term representing an ideal light intensity distribution of the ith optical modulei(x, y) represents an ideal light intensity distribution of the ith optical module on the photoresist,
representing the laguerre basis function of Gauss, sjRepresenting the standard deviation, p, of said Gaussian functionjRepresenting the order of the laguerre polynomial.
7. The method of claim 1,
the fitting error is:
err＝∑|MeasureCD-SimulationCD|2；
where err represents the fitting error, MeasureCDRepresenting the critical dimension measurement data, SimulationCDRepresenting the critical dimension simulation data.
8. A computational lithography modeling apparatus, the apparatus comprising:
the system comprises a graph acquisition module, a graph analysis module and a graph analysis module, wherein the graph acquisition module is used for acquiring the type of a graph unit contained in a test graph, and the test graph refers to a mask graph used for testing;
the optical module group determining module is used for determining an optical module group according to the type of the graphic unit, wherein the optical module group consists of a plurality of optical modules;
the physical optical model parameter acquisition module is used for acquiring parameters of the physical optical model according to the optical module group;
an ideal light intensity calculation module, configured to calculate an ideal light intensity distribution of the optical module group on the photoresist according to the optical module group and the test pattern, where the ideal light intensity distribution includes an ideal light intensity distribution of each of the optical modules on the photoresist;
the photochemical model parameter acquisition module is used for acquiring parameters of a photochemical model according to the ideal light intensity distribution and photochemical reaction excited by the optical module group on the photoresist;
the simulation module is used for acquiring a threshold condition of the photo-resist for photochemical reaction and simulating a boundary position formed by the test pattern on the photo-resist according to the threshold condition and the ideal light intensity distribution;
the data acquisition module is used for acquiring key dimension measurement data of the test pattern and acquiring key dimension simulation data of the test pattern according to the boundary position;
the model establishing module is used for establishing a computational lithography model according to the parameters of the physical optical model and the parameters of the photochemical model when the fitting error between the critical dimension measurement data and the critical dimension simulation data is not larger than a preset allowable error, wherein the computational lithography model comprises the physical optical model and the photochemical model;
wherein the optical module group determination module includes:
the test pattern classification unit is used for classifying the test patterns according to the types of the pattern units;
the proportion obtaining unit is used for obtaining the proportion of each type of test pattern in the test patterns;
the optical module determining unit is used for determining the optical module corresponding to each type of test pattern;
the weight coefficient determining unit is used for determining the weight coefficient of the optical module corresponding to each type of test pattern according to the proportion of each type of test pattern in the test pattern;
and the optical module group determining unit is used for combining the optical modules corresponding to the test patterns according to respective weight coefficients to determine the optical module group.
9. The apparatus of claim 8, further comprising:
and the optimization module is used for re-acquiring the parameters of the physical optical model and the parameters of the photochemical model according to a Newton iteration method and optimizing the computational lithography model when the fitting error is larger than the preset allowable error.
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| CN111258186B (en) * | 2020-03-05 | 2022-02-08 | 上海华力集成电路制造有限公司 | Method for screening light intensity threshold value of SRAF developing on photoresist and predicting risk of SRAF developing by exposure |
| CN114415467B (en) * | 2022-03-29 | 2022-07-05 | 合肥晶合集成电路股份有限公司 | Method and system for acquiring optical proximity effect correction model |
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