CN110554580A - multi-parameter joint optimization method for photoetching machine - Google Patents
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- XUIMIQQOPSSXEZ-UHFFFAOYSA-N Silicon Chemical compound [Si] XUIMIQQOPSSXEZ-UHFFFAOYSA-N 0.000 description 3
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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
Abstract
the invention relates to a multi-parameter joint optimization method for a photoetching machine, which takes photoresist pattern errors at a plurality of depth positions as an objective function and performs joint optimization on the wave fronts, the defocusing amount and the exposure dose of a light source, a mask and a projection objective. And optimizing the light source and the mask by adopting an adaptive differential evolution algorithm. And optimizing the wavefront of the projection objective by adopting a nonlinear least square algorithm. And optimizing the defocus amount and the exposure dose by adopting a dichotomy in a linear search algorithm. The invention effectively improves the quality of the photoresist three-dimensional appearance, enlarges the process window and simultaneously obtains higher optimization efficiency.
Description
Technical Field
The invention relates to a photoetching machine, in particular to a multi-parameter joint optimization method of the photoetching machine.
background
Lithography machines are key devices in the manufacture of very large scale integrated circuits. Resolution is one of the key technical indicators of a lithography machine. Resolution enhancement techniques are important means of enhancing lithographic resolution. The photoetching resolution enhancement technology is developed from single-parameter independent optimization to multi-parameter joint optimization. The multi-parameter joint optimization comprehensively utilizes the interaction of various parameters on the influence of the imaging quality while having higher optimization freedom, and further improves the lithography imaging quality compared with the traditional method for independently optimizing the light source or the mask of the lithography machine.
The optimization algorithm is one of the key factors for determining the optimization effect and efficiency of the advanced resolution enhancement technology. The optimization algorithms used in the existing resolution enhancement technologies are mainly level set (prior art 1. Page Y, Xiao G M, Tolaniv, et al. Considering MEEF in inversion strategy engineering (ILT) and sourcemask optimization (SMO). Proceedings of SPIE,2008,7122:71221W.), conjugate gradient method (prior art 2.Yu J C, Yu P C, Chao H Y. source optimization approach in registration marking of SPIE), genetic algorithm (prior art 3. Yang Kongxing, Li Kun, thought, pixel light source epitaxy method based on the multi-dye genetic algorithm, optical report, optimization 36, 2016 (2016, 36), particle swarm optimization algorithm (prior art 7. Ju, 2016, 7. Queen), particle swarm optimization algorithm (prior art 7, 2016, 7. Queen, Queen), and projection objective algorithm based on the multi-dye genetic algorithm (prior art 2.Yu J C, Yu P C, Chao H Y. source optimization) Augmented Lagrangian methods (prior art 5.Li J, Liu S Y, Lam E Y. effective and mask optimization with an augmented Lagrangian methods in optical compatibility. Opt Express,2013,21(7): 8076-8090), etc. The existing light source mask joint optimization technology and the light source mask projection objective joint optimization technology generally use an algorithm to realize optimization of all parameters, characteristics of optimization variables are not considered, and the optimization speed has an increasable space. Because a large amount of imaging simulation calculation is needed for the joint optimization of a plurality of parameters, the imaging simulation is very time-consuming, and therefore, the method for reducing the imaging simulation times in the optimization process as much as possible is also an effective method for improving the optimization efficiency.
with the continuous reduction of the feature size (CD) of the pattern, the three-dimensional effect of the photoresist causes the photoresist to be partially lost in the vertical direction, so that the etching resistance of the photoresist is reduced. So that the pattern CD after etching is inconsistent with the photoresist pattern CD, the Characteristic Dimension Uniformity (CDU) of the pattern etched on the silicon wafer is reduced, and even the defects such as bridging and the like are generated. Therefore, the three-dimensional shape effect of the photoresist needs to be considered in the resolution enhancement technology. Especially, the process nodes of 28nm and higher need to ensure that the three-dimensional photoresist has higher quality, and the defects caused by the fact that CDU is reduced after etching due to the three-dimensional effect of the photoresist are avoided. In prior art 6 (prior art 6.a.chen, y.m.fong, m.hsieh, a.khoh, s.hsu, et al, resist profile aware mask optimization, proc.spie,2014,9053,90530X.) a light source mask joint optimization technique is proposed that considers the three-dimensional topography of the photoresist, but in the optimization process, a space image is used to indirectly evaluate the three-dimensional topography quality of the photoresist, and the effect has a liftable space.
disclosure of Invention
The invention provides a multi-parameter joint optimization method for a photoetching machine. The method takes the photoresist pattern errors at a plurality of depth positions as an objective function, and performs combined optimization on the light source, the mask, the wavefront of the projection objective, the defocusing amount and the exposure dose. According to the characteristics of each parameter, a light source and a mask are optimized by adopting a self-adaptive differential evolution algorithm, the wave front of a projection objective is optimized by adopting a Levenberg-Marquardt algorithm in a nonlinear least square algorithm, and the defocus and the exposure dose are optimized by adopting a bisection method in a one-dimensional linear search algorithm. The invention effectively improves the quality of the photoresist three-dimensional appearance, enlarges the process window and simultaneously obtains higher optimization efficiency.
The technical solution of the invention is as follows:
The multi-parameter joint optimization method of the photoetching machine sequentially performs exposure dose optimization, defocusing amount optimization, mask optimization, projection objective wavefront optimization and light source optimization, and comprises the following steps of:
initializing an imaging model and optimizing algorithm parameters:
the light source initial value is set to a common ring light source, a circular light source, a quadrupole light source, a dipole light source, or a randomly generated light source.
An initial value of the mask is set as a target mask. And respectively encoding the light source and the mask into a light source vector and a mask vector according to respective encoding methods.
And setting a projection objective wave aberration optimization item, a projection objective wave aberration parameter initial value and an optimization range. The wave aberration optimization item of the projection objective is set as an adjustable wave aberration item in the photoetching machine, the initial value is set as 0, and the optimization range is set as an adjustable range specified in the photoetching machine parameters.
setting initial values and optimization ranges of exposure dose and defocus. The initial value of the exposure dose is set to the exposure dose value determined according to the anchor pattern, and the optimization range is set to be within plus or minus fifty percent of the value. The initial value of the defocus amount is set to 0, and the optimization range is set to the value of the focal depth of the lithography machine.
Setting the maximum number of iterations allowed in the steps from the step two to the step six as N2, N3, N4, N5 and N6 respectively, setting N2, N3, N4, N5 and N6 as natural numbers, and setting the total number of iterations as N, wherein N is a natural number. The evaluation function threshold was set to Cr.
Setting the value of the adaptive parameter, the optimal individual selection proportion and the population scale in the adaptive differential evolution algorithm: setting the value of the adaptive parameter in the adaptive differential evolution algorithm to be between 0.01 and 0.5, setting the optimal individual selection proportion to be between 1 percent and 15 percent, and setting the value of the population scale to be a number which is not less than 5 percent of the total number of the variables to be optimized.
Exposure dose optimization: firstly, setting the current exposure dose value of the imaging model as an initial value, and then adopting dichotomy iterative computation according to the optimization range of the exposure dose to enable the evaluation function to take the exposure dose value of the minimum value. And if the iteration number reaches the set maximum iteration number value N2, outputting the exposure dose value, updating the exposure dose of the imaging model to the exposure dose value, and turning to the step (c). If the evaluation function value reaches the set threshold value, the process proceeds to step (c).
Carrying out defocusing amount optimization: firstly, setting the current defocus value of the imaging model as an initial value, and then adopting dichotomy iterative computation according to the optimization range of the defocus value to enable the evaluation function to take the defocus value of the minimum value. And if the iteration times reach the set maximum iteration number value N3, outputting the defocus value, updating the defocus value of the imaging model into the defocus value, and turning to the step (iv). If the evaluation function value reaches the set threshold value, the process proceeds to step (c).
Fourthly, mask optimization is carried out: firstly, setting the current mask vector as an initial value of one individual in the population of the adaptive differential evolution algorithm, and randomly generating values of other individuals. And then optimizing the mask vector by adopting an adaptive differential evolution algorithm. If the iteration number reaches a set maximum iteration number value N4, outputting the mask vector, and updating the current mask vector into the mask vector; the mask vector is decoded as a mask, the mask in the imaging model is updated as the mask, and the process goes to step (c). If the evaluation function value reaches the set threshold value, the process proceeds to step (c).
Fifthly, projection objective wavefront optimization is carried out: firstly, projecting the current wave aberration parameter value of an imaging model to the wave aberration parameter initial value of an objective lens, then adopting a Levenberg-Marquardt algorithm to iterate and calculate a least square solution, if the iteration number reaches a set maximum iteration number value N5, outputting the current wave aberration parameter value, and turning to the step (c). Updating the wave aberration parameter value of the projection objective in the imaging model to the wave aberration parameter value; if the evaluation function value reaches the set threshold value, the process proceeds to step (c).
Sixthly, optimizing a light source: firstly, setting a current light source vector as an initial value of an individual in a population of a self-adaptive differential evolution algorithm, randomly generating values of other individuals, then optimizing the light source vector by adopting the self-adaptive differential evolution algorithm, outputting the light source vector if the iteration number reaches a set maximum iteration number value N6, updating the current light source vector into the light source vector, decoding the light source vector into a light source, and updating the light source in an imaging model into the light source.
and judging whether the total iteration number reaches a set value or whether the evaluation function threshold reaches a set threshold: and if the total iteration number N or the evaluation function threshold reaches a set value Cr, stopping optimization, and outputting the current exposure dose value, the defocusing amount value, the mask, the projection objective wave aberration and the light source, otherwise, returning to the step.
In the step (I), a light source is described in a pixelization mode, and an encoding method comprises the following steps:
And discretizing the light source into a group of point light sources under the rectangular coordinates of the pupil plane of the illumination system of the photoetching machine. For a light source with symmetry. To ensure four quadrant symmetry of the light source, only point light sources within the first quadrant are encoded. All point light sources are arranged into a light source vector in the order of positive abscissa direction and negative ordinate direction. The encoded light source vector is represented as,
Wherein s isiThe intensity of the light source at the ith point. N is a radical ofsourceRepresenting the total number of point light sources. After normalization with the maximum value, the spot source intensity distribution is between 0 and 1.
for light sources that do not have symmetry. All point sources are encoded. All point light sources are arranged into a light source vector in the order of positive abscissa direction and negative ordinate direction. The coded light source vector is also expressed as formula (1).
In the step (i), the mask is described in a pixelization mode, and the coding method comprises the following steps:
The mask is discretized into a set of points in spatial rectangular coordinates. And arranging all the points into mask vectors according to the sequence along the positive direction of the abscissa and the negative direction of the ordinate, and finishing the coding. The encoded mask vector is represented as,
Wherein m isiThe transmittance at the ith point. N is a radical ofmaskRepresenting the total number of points.
for a mask with symmetry. To ensure mask symmetry, only points within the first quadrant are encoded. All the dots are arranged as a mask vector in order along the positive abscissa direction and the negative ordinate direction. The encoded mask vector is also expressed as equation (2), except that N is the samemaskRepresenting the total number of points in the first quadrant.
The imaging model in the technical solution of the invention is as follows:
the light intensity distribution within the photoresist, i.e., the photoresist internal image, is represented as,
Wherein (x, y) is image plane coordinate, z is depth coordinate in photoresist, (f, g) is pupil plane normalized coordinate, S (f, g) is light source, O (f, g) is mask transmission spectrum, j is imaginary unit, and represents conjugation E0For the incident light vector, H (f, g) is the pupil function of the projection objective.
Wherein n isimageIs the image-side refractive index, M is the projection objective magnification, H0(f, g) is the projection objective stop function, determined by the numerical aperture. Φ (f, g) is the wave aberration. The projection objective wave aberration is expressed by a zernike polynomial:
Wherein the content of the first and second substances,In polar form corresponding to rectangular coordinates (f, g).ZjRepresents a zernike polynomial of the k-th order. c. Ckis the corresponding Zernike coefficient, where c4representing the defocus amount parameter. K represents the total order and has a value of 37. M is a transfer matrix.
And forming a photoresist image after the processes of exposure, postbaking, development and the like. In order to eliminate the influence of the photo-acid diffusion effect in the vertical direction in the photoresist, the photoresist profiles at different depths in the photoresist can be described by using the same threshold model. The above effects are represented using a convolution model:
wherein q (x, y, z) is the concentration distribution of photoacid in the photoresist, and g (σ)zZ) is the convolution kernel, standard deviation σzIs a quantity related to the diffusion length.Representing a convolution. The photoresist profile at any depth within the photoresist can be calculated using a threshold model. In order to ensure the continuity of the optimization process, a sigmoid function is adopted to replace a threshold model to represent the photoresist profile:
Wherein, IProfile(x, y, z) is a photoresist image showing the developed photoresist profile, trthe photoresist threshold is determined by both the photoresist properties and the exposure dose, which for a given photoresist is indicative of the exposure dose, and α is the photoresist sensitivity, determined by the properties of the photoresist itself.
the evaluation function and the calculation method thereof in the technical solution of the invention are as follows:
The sum of the photoresist image pattern errors for a plurality of depth positions within the photoresist is used as an evaluation function. The calculation formula is expressed as
Wherein, IProfile(zi) Denotes the depth in the photoresist as ziPosition resist image, NProfilefor the number of depths sampled, ITargetIs a target graph. In the technical scheme, the optimization process is guided by the evaluation function so as to realize the optimization of the photoresist three-dimensional appearance.
In the method for calculating the evaluation function, when the step (iv) and the step (sixty) are executed, the light source vector and the mask vector need to be decoded, which is the same as the decoding in the step (iv) and the step (sixty), and the specific method is as follows:
for a light source with symmetry, all elements in the light source vector are arranged in the order of positive abscissa and negative ordinate as the light source in the first quadrant. And then, symmetrically operating the light source in the first quadrant to obtain the whole light source. For a light source without symmetry, all elements in the light source vector are arranged as light sources in order along the positive abscissa direction and the negative ordinate direction.
For masks without symmetry, the elements in the mask vector are arranged as a mask in order along the positive abscissa direction and the negative ordinate direction. For a mask with symmetry, all elements in the mask vector are arranged in order along the positive abscissa direction and the negative ordinate direction as a mask in the first quadrant. Then, the mask of the first quadrant is symmetrically operated to obtain the whole mask.
Compared with the prior art, the invention has the following advantages:
1. the method increases the optimization of the defocusing amount and the exposure dose on the basis of the parameters of the light source, the mask and the projection objective, improves the optimization degree of freedom and effectively improves the quality of the three-dimensional shape of the photoresist compared with the prior art.
2. Aiming at the characteristics of different parameters, the invention respectively adopts the self-adaptive differential evolution algorithm, the Levenberg-Marquardt algorithm and the dichotomy to optimize the wavefront, the defocusing amount and the exposure dose of the light source mask and the projection objective, thereby improving the optimization efficiency.
3. According to the method, the photoresist profile is simulated by adopting the rapid photoresist profile model, the evaluation function is established by adopting the photoresist profiles at a plurality of depths to realize the three-dimensional photoresist profile optimization, the representation of the three-dimensional profile is more accurate than that of the prior art, and the photoresist three-dimensional profile optimization effect is effectively improved.
Drawings
FIG. 1 is a schematic diagram of a lithography system;
FIG. 2 is a main flow chart of the present invention;
In fig. 3, (a) is the initial light source, (b) is the initial mask, (c) is the initial projection objective wavefront aberration;
FIG. 4 shows (a) a light source optimized according to the present invention, (b) a mask optimized according to the present invention, and (c) a projection objective wave aberration optimized according to the present invention;
FIG. 5(a) is a cross-sectional view of the photoresist before optimization (b) is a cross-sectional view of the photoresist after optimization by the comparative method (c) is a cross-sectional view of the photoresist after optimization according to the present invention;
FIG. 6 is a comparison of process windows;
Fig. 7 is a graph comparing convergence curves.
Detailed Description
The present invention will be further described with reference to the following examples and drawings, but the scope of the present invention should not be limited by these examples.
FIG. 1 is a schematic diagram of a lithography system used in the present invention. The hardware and materials involved in the method comprise a light source 1 of a photoetching machine, a mask 2, a projection objective 3, an immersion liquid 4, photoresist 5 and a silicon wafer 6. And (4) performing simulation verification by using a line-space pattern mask with the image surface characteristic size of 45nm as a target pattern. The wavelength λ of the light source is 193.368 nm. The projection objective has a numerical aperture of 1.35 and a magnification of 4. The refractive index of the immersion liquid is set to 1.44, the image side refractive index nimageIs 1.44. The photoresist thickness is 94.5nm, the photoresist is positive, the refractive index is 1.719, and the absorption coefficient is 0.3643. The bottom antireflective layer comprises two layers, a silicon-containing antireflective coating and a carbon coating, each having a thickness of 32nm and 200nm, respectively, which have been optimized to minimize reflectivity. The antireflective coating had a refractive index of 1.64 and an absorption coefficient of 0.15. the carbon coating had a refractive index of 1.49 and an absorption coefficient of 0.3. The photoresist model sensitivity parameter α is 50. Kernel function g (σ) in equation (8)zZ) using a Gaussian function, setting σz＝20nm。
The main flow of the invention is shown in fig. 2, and the specific steps are as follows:
Initializing an imaging model and optimizing algorithm parameters. Initial values of the light source, mask, exposure dose, defocus amount, and projection objective wave aberration parameter are set. The initial value of the light source is set to be a ring light source, and as shown in fig. 3(a), the internal coherence factor is 0.6 and the external coherence factor is 0.8. The polarization type is tangential polarization. The light sources were discretized into 51 × 51 point light sources. As shown in FIG. 3(b), the mask initial value was 45nm in feature size and 720nm × 720nm in actual size. Mask type is a 6% attenuated phase shift mask, discretized into 81 x 81 dots. Initial values of wave aberration of the projection objective are shown in FIG. 3(c)As shown, the optical lens does not contain any wave aberration, i.e., all values of Zernike coefficients are set to 0. The light source and the mask are respectively encoded into vectors according to respective encoding methods. The vectors obtained by encoding are referred to as a light source vector and a mask vector, respectively. The optimization term of the wave aberration Zernike coefficient of the projection objective is set as z9、z16、z25、z36Their respective optimum ranges are set to [ -0.1 λ,0.1 λ]. Setting an initial value of exposure dose to tr0.5, the optimum range is set to 0.3,0.8]. The initial value of the defocusing amount is set to-50 nm, and the optimization range is set to-100 nm and 0nm]. In the differential evolution algorithm, the adaptive parameter is set to be 0.1, the optimal individual selection proportion is 5%, and the population scale is 50%. And c, sequentially setting the maximum iteration times of optimizing the wavefront, the defocus amount and the exposure dose of the light source, the mask and the projection objective as N2-100, N3-100, N4-10, N5-10, N6-10 and the total iteration time value N as 5. The evaluation function threshold is set to Cr 250.
And ② optimizing exposure dose. Firstly, setting the current exposure dose value of the imaging model as an initial value, and then adopting dichotomy iterative computation according to the optimization range of the exposure dose to enable the evaluation function to take the exposure dose value of the minimum value. And if the iteration number reaches the set maximum iteration number value N2, outputting the exposure dose value, updating the exposure dose of the imaging model to the exposure dose value, and turning to the step (c). And if the evaluation function value reaches the set threshold value Cr, performing step (c).
And thirdly, optimizing the defocusing amount. Firstly, setting the current defocus value of the imaging model as an initial value, and then adopting dichotomy iterative computation according to the optimization range of the defocus value to enable the evaluation function to take the defocus value of the minimum value. And if the iteration times reach the set maximum iteration number value N3, outputting the defocus value, updating the defocus value of the imaging model into the defocus value, and turning to the step (iv). And if the evaluation function value reaches the set threshold value Cr, performing step (c).
and fourthly, optimizing the mask. Firstly, setting the current mask vector as an initial value of one individual in the population of the adaptive differential evolution algorithm, and randomly generating values of other individuals. And then optimizing the mask vector by adopting an adaptive differential evolution algorithm. If the iteration number reaches the set maximum iteration number value N4, the mask vector is output. The current mask vector is updated to the mask vector. The mask vector is decoded into a mask. The mask in the imaging model is updated to the mask. Go to step (v). And if the evaluation function value reaches the set threshold value Cr, performing step (c).
and fifthly, performing wavefront optimization on the projection objective. Firstly, the current wave aberration parameter value of the imaging model is projected to the wave aberration parameter initial value of the objective lens. And then iteratively calculating a least square solution by adopting a Levenberg-Marquardt algorithm. If the iteration number reaches the set maximum iteration number value N5, the current wave aberration parameter value is output. Go to step (c). And updating the wave aberration parameter value of the projection objective in the imaging model to the wave aberration parameter value. And if the evaluation function value reaches the set threshold value Cr, performing step (c).
Sixthly, optimizing the light source. Firstly, setting the current light source vector as an initial value of one individual in a population of the self-adaptive differential evolution algorithm, and randomly generating values of other individuals. And then, optimizing the light source vector by adopting a self-adaptive differential evolution algorithm. And if the iteration number reaches the set maximum iteration number value N6, outputting the light source vector. And updating the current light source vector to the light source vector. The illuminant vector is decoded into an illuminant. And updating the light source in the imaging model to the light source.
and judging whether the total iteration number reaches a set value N or whether the evaluation function threshold reaches a set threshold Cr. And if the total iteration number or the evaluation function threshold value reaches a set value, stopping optimization, and outputting the current exposure dose value, the defocusing amount value, the mask, the projection objective wave aberration and the light source. Otherwise, repeating the steps from (II) to (III)
in the step (I), a light source is described in a pixelization mode, and an encoding method comprises the following steps:
the light source is discretized into 51 × 51 point light sources under the rectangular coordinates of the pupil plane of the illumination system of the photoetching machine. Because the light source is a symmetrical light source, only the point light source in the first quadrant is coded in order to ensure the four-quadrant symmetry of the light source. And arranging all point light sources in the first quadrant into light source vectors according to the sequence along the positive direction of the horizontal coordinate and the negative direction of the vertical coordinate, and finishing coding. The encoded light source vector is represented as:
Wherein s isiThe intensity of the light source at the ith point. N is a radical ofsourceRepresenting the total number of point sources located in the first quadrant. After normalization with the maximum value, the spot source intensity distribution is between 0 and 1.
In the step (i), the mask is described in a pixelization mode, and the coding method comprises the following steps:
The mask was discretized into 81 x 81 points in spatial rectangular coordinates. Since the mask is a symmetric mask, only the points in the first quadrant are encoded in order to ensure symmetry of the mask. And arranging all points in the first quadrant into mask vectors according to the sequence along the positive direction of the abscissa and the negative direction of the ordinate, and finishing the coding. The encoded mask vector is represented as,
Wherein m isiThe transmittance at the ith point. N is a radical ofmaskRepresenting the total number of points located in the first quadrant.
the imaging model in the technical solution of the invention is as follows:
The light intensity distribution within the photoresist, i.e., the photoresist internal image, is represented as,
wherein, (x, y) is the image plane coordinate, z is the depth coordinate in the photoresist, (f, g) is the pupil plane normalized coordinate, S (f, g) is the light source, O (f, g) is the mask transmission spectrum, j is the imaginary unit, and x represents the conjugate. E0For the incident light vector, H (f, g) is the pupil function of the projection objective.
wherein n isimageis the image-side refractive index, M is the projection objective magnification, H0(f, g) is the projection objective stop function, and Φ (f, g) is the wave aberration. The projection objective wave aberration is expressed by a zernike polynomial:
Wherein the content of the first and second substances,In polar form corresponding to rectangular coordinates (f, g).ZjRepresents a zernike polynomial of the k-th order. c. CkThe corresponding zernike coefficients. K represents the total order and has a value of 37. M is a transfer matrix of the projection objective, and is obtained by calculation according to the existing method after the photoresist and the materials of the lower layers are given. The switching relationship of the pupil plane and the image plane electric field is described.
Finally forming a photoresist image through the processes of exposure, postbaking, development and the like. In order to eliminate the influence of the photo-acid diffusion effect in the vertical direction in the photoresist, the photoresist profiles at different depths in the photoresist can be described by using the same threshold model. The above effects are represented using a convolution model:
Wherein q (x, y, z) is the concentration distribution of photoacid in the photoresist, and g (σ)zZ) is the convolution kernel, standard deviation σzis a quantity related to the length of the diffusion,Representing a convolution. The photoresist profile at any depth within the photoresist can be calculated using a threshold model. To ensureand (3) confirming the continuity of the optimization process, and representing the photoresist profile by adopting a sigmoid function instead of a threshold model:
wherein, IProfile(x, y, z) is a photoresist image showing the developed photoresist profile, trAlpha is the photoresist threshold and the photoresist sensitivity.
The evaluation function and the calculation method thereof in the technical solution of the invention are as follows:
The sum of the figure errors of the photoresist image at three depth positions of 10%, 50% and 90% height in the photoresist is used as the evaluation function. The calculation formula is expressed as
Wherein, IProfile(zi) Denotes the depth in the photoresist as ziposition resist image, NProfileFor the number of depths sampled, this example equals 3, ITargetIs a target graph. In the technical scheme, the optimization process is guided by the evaluation function so as to realize the optimization of the photoresist three-dimensional appearance.
In the method for calculating the evaluation function, when the step (iv) and the step (sixty) are executed, the light source vector and the mask vector need to be decoded, which is the same as the decoding in the step (iv) and the step (sixty), and the specific method is as follows:
And arranging all elements in the light source vector into a light source positioned in the first quadrant according to the sequence along the positive direction of the abscissa and the negative direction of the ordinate. And then, symmetrically operating the light source in the first quadrant to obtain the whole light source.
And arranging all elements in the mask vector into a mask positioned in a first quadrant according to the sequence along the positive direction of the abscissa and the negative direction of the ordinate, and then carrying out symmetrical operation on the mask in the first quadrant to obtain the whole mask.
After optimization, the conditions in the embodiment are adoptedThe light source, mask, projection objective wavefront of (a) are shown in fig. 4(a), fig. 4(b) and fig. 4(c), respectively. After optimization trthe value of (A) is 0.3867, and the defocus amount is-67.81 nm. The merit function before optimization was 1796.4, and after optimization the merit function was reduced to 253.2. And adopting a light source mask projection objective joint optimization technology based on the photoresist profile at a single depth position before optimization as a comparison method. The cross-sectional view of the three-dimensional topography of the photoresist before optimization is shown in fig. 5(a), fig. 5(b) is the cross-sectional view of the three-dimensional topography of the photoresist after optimization by adopting a light source mask projection objective joint optimization technology based on a photoresist profile at a single depth position, and fig. 5(c) is the cross-sectional view of the three-dimensional topography of the photoresist obtained after optimization according to the invention. The contrast shows that the photoresist side wall is steeper after the optimization, the CD value is closer to the target value, and the appearance quality is better. Figure 6 shows the process window before and after optimization. The calculated position of the process window is the position of 10% of the photoresist thickness, as indicated by the line segment in fig. 5. The CD margin is set to 8%. The comparison shows that the invention obtains the largest process window after being implemented, and the maximum available focal depth and the exposure margin can respectively reach 237nm and 18.05 percent.
in order to verify that the method has a fast convergence rate. A multi-parameter joint optimization method based on a self-adaptive differential evolution algorithm is adopted as a comparison method, namely, a light source, a mask, the wavefront of a projection objective, the defocus amount and the exposure dose are uniformly optimized by adopting the differential evolution algorithm, and other technical schemes and parameter input are the same as those of the method. The convergence curves for both methods are shown in fig. 7. At an optimization time of 12000 seconds, the evaluation function value of the comparative method was 160.0, and the evaluation function value of the present invention was 132.9. Compared with the method, the time for reaching the solution with the evaluation function of 200 is 7197 seconds, but the method only needs 2846 seconds, which shows that the technical scheme of adopting different optimization algorithms according to the characteristics of different parameters in the method has higher speed and higher optimization efficiency.
Claims (6)
1. a multi-parameter joint optimization method for a lithography machine is characterized by comprising the following steps:
initializing an imaging model and optimizing algorithm parameters:
The initial value of the light source is set to be a common annular light source, a circular light source, a quadrupole light source, a dipolar light source or a randomly generated light source;
Setting an initial value of a mask as a target mask; respectively encoding the light source and the mask into a light source vector and a mask vector according to respective encoding methods;
setting a projection objective wave aberration optimization item, a projection objective wave aberration parameter initial value and an optimization range: the wave aberration optimization item of the projection objective is set as an adjustable wave aberration item in the photoetching machine, the initial value is set as 0, and the optimization range is set as an adjustable range specified in parameters of the photoetching machine;
Setting initial values and optimization ranges of exposure dose and defocus: the initial value of the exposure dose is set as the exposure dose value determined according to the anchor graph, the optimization range is set within the range of fifty percent plus or minus the value, the initial value of the defocus amount is set as 0, and the optimization range is set as the value of the depth of focus of the photoetching machine;
Setting the maximum number of iterations allowed in the steps from the step two to the step six as N2, N3, N4, N5 and N6 respectively, setting N2, N3, N4, N5 and N6 as natural numbers, setting the total number of iterations as N, setting N as a natural number, and setting an evaluation function threshold as Cr;
Setting the value of the adaptive parameter, the optimal individual selection proportion and the population scale in the adaptive differential evolution algorithm: setting the value of the adaptive parameter in the adaptive differential evolution algorithm to be between 0.01 and 0.5, setting the optimal individual selection proportion to be between 1 percent and 15 percent, and setting the value of the population scale to be not less than 5 percent of the total number of the variables to be optimized;
exposure dose optimization: firstly, setting the current exposure dose value of an imaging model as an initial value, then adopting dichotomy iterative computation according to the optimization range of the exposure dose to enable the evaluation function to take the exposure dose value of the minimum value, outputting the exposure dose value if the iteration number reaches the set maximum iteration number value N2, updating the exposure dose of the imaging model into the exposure dose value, and turning to the step (c); if the evaluation function value reaches the set threshold value, entering step (c);
Carrying out defocusing amount optimization: firstly, setting the current defocus value of the imaging model as an initial value, then adopting dichotomy iterative computation according to the optimization range of the defocus value to enable the evaluation function to take the defocus value with the minimum value, outputting the defocus value if the iteration number reaches the set maximum iteration number value N3, updating the defocus value of the imaging model into the defocus value, and turning to the fourth step; if the evaluation function value reaches the set threshold value, entering step (c);
Fourthly, mask optimization is carried out: firstly, setting a current mask vector as an initial value of an individual in a population of the adaptive differential evolution algorithm, randomly generating values of other individuals, then optimizing the mask vector by adopting the adaptive differential evolution algorithm, outputting the mask vector if the iteration number reaches a set maximum iteration number value N4, and updating the current mask vector into the mask vector; decoding the mask vector to be a mask, updating the mask in the imaging model to be the mask, and turning to the fifth step; if the evaluation function value reaches the set threshold value, entering step (c);
fifthly, projection objective wavefront optimization is carried out: firstly, projecting the current wave aberration parameter value of an imaging model to the wave aberration parameter initial value of an objective lens, then adopting a Levenberg-Marquardt algorithm to iterate and calculate a least square solution, if the iteration number reaches a set maximum iteration number value N5, outputting the current wave aberration parameter value, and turning to the step (c); updating the wave aberration parameter value of the projection objective in the imaging model to the wave aberration parameter value; if the evaluation function value reaches the set threshold value, entering step (c);
Sixthly, optimizing a light source: firstly, setting a current light source vector as an initial value of an individual in a population of a self-adaptive differential evolution algorithm, randomly generating values of other individuals, then optimizing the light source vector by adopting the self-adaptive differential evolution algorithm, outputting the light source vector if the iteration number reaches a set maximum iteration number value N6, updating the current light source vector into the light source vector, decoding the light source vector into a light source, and updating the light source in an imaging model into the light source;
and judging whether the total iteration number reaches a set value or whether the evaluation function threshold reaches a set threshold: and if the total iteration number N or the evaluation function threshold reaches a set value Cr, stopping optimization, and outputting the current exposure dose value, the defocusing amount value, the mask, the projection objective wave aberration and the light source, otherwise, returning to the step.
2. The multi-parameter joint optimization method of lithography machine according to claim 1, wherein the encoding method of the light source is:
discretizing a light source into a group of point light sources under a pupil plane rectangular coordinate of a photoetching machine illumination system, only coding the point light sources in a first quadrant in order to ensure the four-quadrant symmetry of the light source, arranging all the point light sources into light source vectors according to the sequence of positive directions of horizontal coordinates and negative directions of vertical coordinates, finishing coding, and expressing the coded light source vectors as follows:
Wherein s isiis the intensity of the ith point light source, NsourceRepresenting the total number of point light sources in the first quadrant, the intensity distribution of the point light sources is between 0 and 1 after normalization by a maximum value.
3. the multi-parameter joint optimization method of lithography machine according to claim 1, characterized in that the mask encoding method is:
discretizing the mask into a group of points under a space rectangular coordinate, arranging all the points into mask vectors according to the sequence along the positive direction of a horizontal coordinate and the negative direction of a vertical coordinate, and expressing the coded mask vectors as follows:
Wherein m isiThe transmittance at the ith point. N is a radical ofmaskRepresenting the total number of points.
4. The multi-parameter joint optimization method of lithography machine according to claim 1, wherein the imaging model is the light intensity distribution in the photoresist, i.e. the image in the photoresist, expressed as:
wherein (x, y) is image plane coordinate, z is depth coordinate in photoresist, (f, g) is pupil plane normalized coordinate, S (f, g) is light source, O (f, g) is mask transmission spectrum, j is imaginary unit, and represents conjugation E0for the incident light vector, H (f, g) is the pupil function of the projection objective:
wherein n isimageis the image-side refractive index, M is the projection objective magnification, H0(f, g) is the projection objective aperture function, determined by the numerical aperture, phi (f, g) is the wave aberration, which is expressed by zernike polynomials as follows:
wherein the content of the first and second substances,in polar form corresponding to rectangular coordinates (f, g),Zkdenotes a Zernike polynomial of the k-th order, ckIs the corresponding Zernike coefficient, where c4Expressing a defocus parameter, K expressing a total order, wherein the value of K is 37, and M is a transfer matrix;
forming a photoresist image after the processes of exposure, postbaking, development and the like, and in order to eliminate the influence of the photoacid diffusion effect in the vertical direction in the photoresist, enabling the photoresist profiles of different depths in the photoresist to be described by adopting the same threshold model, and expressing the above effects by adopting a convolution model:
Wherein q (x, y, z) is the concentration distribution of photoacid in the photoresist, and g (σ)zZ) is the convolution kernel, standard deviation σzIs a quantity related to the length of the diffusion,representing convolution, calculating the photoresist profile of any depth in the photoresist by adopting a threshold model, and representing the photoresist profile by adopting a sigmoid function instead of the threshold model in order to ensure the continuity of an optimization process:
Wherein, IProfile(x, y, z) is a photoresist image showing the developed photoresist profile, trThe photoresist threshold is determined by both the photoresist properties and the exposure dose, which for a given photoresist is indicative of the exposure dose, and α is the photoresist sensitivity, determined by the properties of the photoresist itself.
5. The multi-parameter joint optimization method of the lithography machine according to claim 1, wherein the evaluation function and the calculation method thereof are as follows:
The sum of the figure errors of the photoresist at a plurality of depth positions in the photoresist is used as an evaluation function, and the calculation formula of the evaluation function F is as follows:
Wherein, IProfile(zi) Denotes the depth in the photoresist as ziposition resist image, NProfilefor the number of depths sampled, ITargetIs a target graph.
6. the multi-parameter joint optimization method of the lithography machine according to claim 1, wherein the decoding method of the evaluation function is as follows:
Arranging all elements in the light source vector into a light source positioned in a first quadrant according to the sequence along the positive direction of a horizontal coordinate and the negative direction of a vertical coordinate, and then symmetrically operating the light source in the first quadrant to obtain the whole light source;
The elements in the mask vector are arranged as a mask in the order of positive abscissa and negative ordinate.
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