CN113495435B - Digital mask projection lithography optimization method and system - Google Patents
Digital mask projection lithography optimization method and system Download PDFInfo
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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
- G03F7/70216—Mask projection systems
- G03F7/70283—Mask effects on the imaging process
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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
- G03F7/70508—Data handling in all parts of the microlithographic apparatus, e.g. handling pattern data for addressable masks or data transfer to or from different components within the exposure apparatus
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T10/00—Road transport of goods or passengers
- Y02T10/10—Internal combustion engine [ICE] based vehicles
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Abstract
The invention provides a digital mask projection light for solving the problems that the actual photoetching pattern deviates from the target design pattern and the photoetching resolution is difficult to improve in digital mask projection photoetchingThe method and the system for optimizing the etching comprise the following steps: establishing a matrix expression of complex amplitude distribution of the digital mask, and constructing a digital mask projection lithography imaging model; establishing a cost function F with digital mask as a variable and related to the fidelity of the graph; given binary target graphicsCarrying out digital mask inversion calculation on the digital mask projection lithography imaging model, calculating the gradient of the digital mask based on the cost function F, optimizing the digital mask projection lithography imaging model, and stopping iteration after a certain number of iterations or certain conditions are met to obtain a digital mask M; loading the digital mask M on a spatial light modulator to obtain a pattern corresponding to the target patternThe lithographic pattern Z with the smallest gap.
Description
Technical Field
The invention relates to the technical field of digital mask projection lithography, in particular to a layout optimization method and system for digital mask projection lithography.
Background
As lithographic feature sizes decrease, the lithographic pattern will be severely distorted, so inversion lithography (Inverse Lithography Technology, ILT) is commonly used in conventional mask lithography to account for image distortion and to improve the resolution of the lithographic pattern. The conventional photoetching mostly adopts inversion calculation mask optimization and correction based on pixel characterization, and the essence of the method is that complex amplitude transmittance of each sampled pixel point is optimized, and the optimized graph is of a complex topological structure, so that manufacturing difficulty and cost of the mask are increased, and certain graphs cannot be manufactured. Therefore, the commercial inversion lithography software can restrict the manufacturing rule of the mask to ensure the manufacturability of the mask, but the optimized mask can be influenced unpredictably, such as feature size errors, pattern placement errors and the like.
In the prior maskless projection lithography technology based on a Spatial Light Modulator (SLM), on one hand, the cost of a mask plate and manufacturing equipment thereof can be saved because the cost of a digitalized mask is far lower than that of a traditional solid mask manufactured on the basis of electron beam lithography; on the other hand, the digital mask can generate any complex topological structure, is not limited by the optimized manufacturing rule of the traditional photoetching mask, and can obviously improve the manufacturability, flexibility and production efficiency of the photoetching pattern, so that the technology is widely focused on the small-batch and customized production application fields of industry, national defense and the like. However, as maskless projection lithography feature sizes shrink, the lithographic pattern still deviates significantly from the designed pattern, or there is a problem of lower resolution in digital mask projection lithography. Therefore, proximity effect correction based on inverse lithography is required for digital masks, but conventional mask inversion calculation lithography algorithms are not directly applicable to optimization of discretized digital masks.
Disclosure of Invention
The invention provides a digital mask projection photoetching optimization method and a digital mask projection photoetching optimization system, which are used for solving the problems that the actual photoetching pattern deviates from the target design pattern and the photoetching resolution is difficult to improve in the existing digital mask projection photoetching.
In order to solve the technical problems, the technical scheme of the invention is as follows:
a digital mask projection lithography optimization method, comprising the steps of:
establishing a matrix expression of complex amplitude distribution of the digital mask, and constructing a digital mask projection lithography imaging model;
establishing a cost function F with digital mask as a variable and related to the fidelity of the graph;
given binary target graphicsPerforming digital mask inversion calculation on the digital mask projection lithography imaging model, calculating the gradient of the digital mask based on the cost function F, and performing iterative optimization on the digital mask projection lithography imaging model to obtain a digital mask M;
the numbers are processedThe mask M is loaded on the spatial light modulator to obtain the pattern corresponding to the targetThe lithographic pattern Z with the smallest gap.
Preferably, the digital mask projection lithography imaging model includes an optical model and a chemical model of photoresist.
Preferably, the chemical model of the photoresist is expressed as:
wherein a is r The larger the value of the constant coefficient is, the closer the sigmoid function is to the hard threshold function; t is t r Is a photoresist threshold; z (x, y) has a value between 0 and 1; i (x, y) represents a light source imaging model, and the expression formula is as follows:
in the formula, h p (x, y) represents the point spread function in the x, y, z polarization directions, and m (x, y) represents the complex amplitude transmittance of the digital mask; * Representing a convolution operation.
Preferably, the light source imaging model I (x, y) comprises a linear superposition of coherent system light intensities in the polarization direction.
Preferably, the digital mask is generated by an amplitude spatial light modulator, and the complex amplitude transmittance m (x, y) of the digital mask is expressed as:
wherein a is m,n (x-md x ,y-nd y ) Representing the light field modulation at the pixel point (m, n), and the amplitude of the light field modulation is any real number from 0 to 1 after normalization, and the phase is 0 or pi; u (x-md) x ,y-nd y ) Representing the pixel point (m, n)Complex amplitude transmittance, u function is rectangular function; d, d x 、d y Respectively representing the x-direction period and the y-direction period of the pixel arrangement;
when the matrix expression of the complex amplitude distribution with the digital mask is established, the expression is:
in the method, in the process of the invention,in the form of a discrete matrix of complex amplitude transmittance m (x, y) of a digital mask, +.>Is a as m,n (x-md x ,y-nd y ) Is a matrix expression of core as u (x-md x ,y-nd y ) Representing a sampling matrix of individual pixels of the digital mask; />Representing the kronecker product.
As a preferable scheme, an optical model of the digital mask projection lithography imaging model is established by using a discrete matrix of the digital mask complex amplitude transmittance, and the expression formula is as follows:
the generated lithographic pattern Z is expressed as:
where T { M } represents the lithography forward system and represents the lithography pattern obtained by receiving the digital mask M.
Preferably, the digital mask is inverted and calculatedIn the course, for a given binary target graphFind a digital mask->And loaded on the spatial light modulator such that the lithographic patternIs +.>The difference between (2) is the smallest, and the cost function F is expressed as:
wherein N is M Representing the number of pixels of the digital mask pixels arranged in either the x or y direction;representing the square of the F-norm.
Preferably, in the digital mask inversion calculation process, when the digital mask is only loaded with gray amplitude and the phase is not modulated, the pixel M of the ith row and the jth column of the digital mask M i,j ∈[0,1]Wherein i, j=1, 2, N M There is an optimization problem:
wherein, the liquid crystal display device comprises a liquid crystal display device,
when the digital mask is loaded with gray amplitude and its bit is 0 or pi, the element M of the ith row and jth column of the digital mask M i,j ∈[-1,1]Where i, j=1, 2.,N M There is an optimization problem:
M i,j ＝cosθ i,j
wherein, the liquid crystal display device comprises a liquid crystal display device,θ i,j ∈[-∞,+∞]the method comprises the steps of carrying out a first treatment on the surface of the In θ i,j Pixels M representing the ith row and jth column of the digital mask M i,j Corresponding discrete matrix elements.
In the optimization process of the digital mask projection lithography imaging model, the gradient of the cost function F to the digital mask is calculated by adopting a steepest descent method according to the optimization problem.
The digital mask projection lithography optimization system is applied to the digital mask projection lithography optimization method according to any one of the above technical schemes, and comprises an on-axis point light source, a spatial light modulator and a processor, wherein: the processor executes the steps of the digital mask projection lithography optimization method according to any one of the above technical schemes; the on-axis point light source generates an optimized digital mask M through the processor and then loads the optimized digital mask M on the spatial light modulator to obtain a target graphThe lithographic pattern Z with the smallest gap.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that: the invention uses a spatial light modulator to realize a digital mask, replaces an expensive mask plate of a traditional photoetching system, builds a digital mask projection photoetching imaging model aiming at the digital mask, and further adopts a digital mask inversion calculation photoetching technology to solve the complex amplitude modulation coefficient loaded by each pixel of the digital mask (namely, solve a digital mask) so as to ensure that the corresponding photoetching pattern Z and the expected target patternAnd the resolution ratio of digital mask projection lithography can be effectively improved.
Drawings
FIG. 1 is a flow chart of a digital mask projection lithography optimization method of embodiment 1.
Fig. 2 is a schematic diagram of the # -operation of embodiment 1.
Fig. 3 is a graph showing the amplitude of the point spread function of the x-direction polarization of the point light source of example 1.
Fig. 4 is a graph showing the amplitude of the point spread function of the y-direction polarization of the point light source of example 1.
Fig. 5 is a graph showing the amplitude of the point spread function of the point light source z-direction polarization of example 1.
FIG. 6 is a schematic view of the L-shaped lithography pattern and its digital mask projection lithography optimization of example 2.
Fig. 7 is a schematic diagram of the grating pattern and the digital mask projection lithography optimization of example 2.
FIG. 8 is a schematic diagram of a typical lithographic pattern and its digital mask projection lithography optimization of example 2.
FIG. 9 is another exemplary lithographic pattern and digital mask projection lithography optimization schematic of example 2.
FIG. 10 is another exemplary lithographic pattern and digital mask projection lithography optimization schematic of example 2.
FIG. 11 is a schematic diagram of a digital mask projection lithography optimization system of example 3.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the present patent;
for the purpose of better illustrating the embodiments, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the actual product dimensions;
it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.
Example 1
The present embodiment proposes a digital mask projection lithography optimization method, as shown in fig. 1, which is a flowchart of the digital mask projection lithography optimization method of the present embodiment.
The digital mask projection lithography optimization method provided by the embodiment comprises the following steps:
step 1: a matrix expression of complex amplitude distribution of the digital mask is established, and a digital mask projection lithography imaging model is constructed.
The digital mask in this embodiment is generated by a spatial light modulator, and the complex amplitude transmittance m (x, y) of the digital mask is expressed as:
wherein a is m,n (x-md x ,y-nd y ) Representing the light field modulation at the pixel point (m, n), and the amplitude of the light field modulation is any real number from 0 to 1 after normalization, and the phase is 0 or pi; d, d x 、d y Respectively representing the pixel periods in the x and y directions; u (x-md) x ,y-nd y ) Representing the complex amplitude transmittance at pixel points (m, n), and the u-function is a rectangular function because the spatial light modulator is generally composed of a rectangular periodic arrangement of small pixels.
Thus, in this step, when the matrix expression of the complex amplitude distribution with the digital mask is established, the expression is:
in the method, in the process of the invention,in the form of a discrete matrix of complex amplitude transmittance m (x, y) of a digital mask, +.>Is a as m,n (x-md x ,y-nd y ) Is a matrix expression of core as u (x-md x ,y-nd y ) Representing a sampling matrix of individual pixels of the digital mask; />Represents the kronecker product (Kronecker Product).
In this embodiment, considering the specificity of the digital mask, the complex amplitude transmittance of the digital mask to light in different directions may be different, that is, the validity of the off-axis illumination of the illumination mode of the conventional mask cannot be verified, so in order to ensure the normal operation of the spatial light modulator, an on-axis point light source is used for illumination, and then the light source imaging model of the digital mask projection lithography system is expressed as:
in the formula, h p (x, y) represents the point spread function in the x, y, z polarization directions, and m (x, y) represents the complex amplitude transmittance of the digital mask; * Representing a convolution operation. And the light source imaging model I (x, y) in the embodiment is a linear superposition of the light intensity of the coherent system in three polarization directions of x, y and z.
Further, the digital mask projection lithography imaging model of the present embodiment includes a chemical model and an optical model of the photoresist.
For a chemical model of photoresist, generally, the photoresist (negative photoresist is taken as an example in the embodiment) reaches an exposure threshold when receiving light intensity, and photoresist molecules are crosslinked and insoluble in a developing solution and remain as a photoresist pattern; the hard threshold model is as follows:
wherein Z is b Representation, I r Is a photoresist threshold; from the above, Z b In order to be binary and the expression of the photoresist is not conductive, in the inversion calculation lithography technology, in order to be conductive by a cost function, a sigmoid function is used to replace a hard threshold function in the embodiment, and then the chemical model of the photoresist in the embodiment is expressed as follows:
wherein a is r The larger the value of the constant coefficient is, the closer the sigmoid function is to the hard threshold function; t is t r Is a photoresist threshold; the value of Z (x, y) is between 0 and 1. The function is that if the received light intensity of a pixel point is greater than the photoresist threshold t r The closer its value is to 1, representing the exposure of that location; if the received light intensity of a pixel point is smaller than the photoresist threshold t r The closer the value is to 0, which means that the location is not exposed.
In this embodiment, an optical model of a digital mask projection lithography imaging model is built by using a discrete matrix of digital mask complex amplitude transmittance, and the expression formula is as follows:
the generated lithographic pattern Z is expressed as:
where T { M } represents the lithography forward system and represents the lithography pattern obtained by receiving the digital mask M.
Step 2: a cost function F relating to the fidelity of the pattern is established with the digital mask as a variable.
In the digital mask inversion calculation process of the present embodiment, for a given binary target patternFind a digital mask->And loaded on the spatial light modulator such that the lithographic pattern ZεR N×N Is +.>Minimum gap of (2)The cost function F is expressed as:
wherein N is M Representing the number of pixels arranged in the x or y direction of the digital mask;the square of the F norm is shown, and the lithography pattern Z and the target pattern are shown +.>Square of the euler distance of (c). The cost function F takes the digital mask M as a variable, so that the cost function F characterizes the lithography pattern Z obtained by the digital mask M and the target pattern +.>The smaller the value of the difference, the closer the resulting lithographic pattern Z is to the target pattern +.>
Step 3: given binary target graphicsAnd carrying out digital mask inversion calculation on the digital mask projection lithography imaging model, calculating the gradient of the digital mask based on the cost function F, optimizing the digital mask projection lithography imaging model, and stopping iteration after a certain number of iterations or a certain condition is met to obtain the digital mask M.
In this embodiment, when the digital mask is only loaded with gray-scale amplitude and the phase is not modulated, the element M of the ith row and jth column of the digital mask M i,j ∈[0,1]Wherein i, j=1, 2, N M For constrained optimization solution difficulties, the present embodiment uses trigonometric functions to transform the problem into an unconstrained optimization problem:
wherein, the liquid crystal display device comprises a liquid crystal display device,θ i,j ∈[-∞,+∞]，i,j＝1,2,...,N M the method comprises the steps of carrying out a first treatment on the surface of the Wherein θ represents a digital mask, θ i,j A digital mask discrete matrix element representing an ith row and a jth column;
the steepest descent method is used to calculate the gradient of the cost function F with respect to the digital mask M, i.e. the gradient of the cost function F with respect to the digital mask θ:
when the digital mask is loaded with gray scale amplitude and its bit is 0 or pi, the element M of the ith row and jth column in the digital mask M i,j ∈[-1,1]Wherein i, j=1, 2, N M For constrained optimization solution difficulties, the present embodiment uses trigonometric functions to transform the problem into an unconstrained optimization problem:
M i,j ＝cosθ i,j
wherein, the liquid crystal display device comprises a liquid crystal display device,θ i,j ∈[-∞,+∞]，i,j＝1,2,...,N M the method comprises the steps of carrying out a first treatment on the surface of the The steepest descent method is used to calculate the gradient of the cost function F with respect to the digital mask M, i.e. the gradient of the cost function F with respect to the digital mask θ:
wherein a is r Parameters representing sigmoid functions; re { · } represents the real part;representation pair matrix h p Is turned over up and down, left and right; h is a p * Representation pair matrix h p Is a conjugate operation; />Representing the corresponding multiplication of matrix elements; core represents a core matrix; t represents a target lithography pattern;
the operation defined by the embodiment shows that the sampling points in each pixel are multiplied by matrix elements in a core matrix (sampling matrix of a single pixel of a digital mask) correspondingly and then added, and then a new matrix is formed according to the original arrangement sequence; if the core matrix is the full 1 matrix, the operation is equal to the average pooling, and the gradient calculation is the down-sampling process because the kronecker product with the full 1 matrix is equal to the up-sampling process.
As shown in fig. 2, a schematic diagram of the # -operation in this embodiment is shown. The core matrix shown as 3 x 3 in the figure is operated with the 6 x 6 matrix, and assuming that the 6 x 6 matrix is the gradient of each sampling point of the digital mask with respect to F, the sampling points of the same color come from the same digital mask pixel, and since the characteristic of the light in the amplitude space can only modulate the amplitude of each individual pixel, the amplitude of different positions in the pixel cannot be modulated, and therefore, the values of the sampling points from the same digital mask pixel must also be kept consistent. The present embodiment uses a (or) operation to keep the sampling points within a "region" of one pel size of the digital mask consistent during the iterative process.
Further, the present embodiment calculates the gradient of the cost function F with respect to the digital mask by using the steepest descent method. The steepest descent method generally uses the opposite direction of the gradient as the iteration direction directly, and uses accurate search or inaccurate line search as the step length, or constant step length; in the embodiment, the value of the digital mask is continuously iterated by adopting a steepest descent method, the digital mask projection lithography imaging model is optimized, and iteration is stopped after a certain number of iterations or certain conditions are met, so that the digital mask M is obtained.
Step 4: loading the digital mask M on a spatial light modulator to obtain a pattern corresponding to the target patternThe lithographic pattern Z with the smallest gap.
The digital mask projection lithography optimization method provided by the embodiment uses a spatial light modulator to realize a digital mask, replaces an expensive mask plate of a traditional lithography system, constructs a digital mask projection lithography imaging model for the digital mask, and further adopts a digital mask inversion calculation lithography technology to solve complex amplitude modulation coefficients loaded by each pixel of the digital mask (namely, solve a digital mask) so as to ensure that the corresponding lithography pattern Z and a desired target patternAnd the resolution ratio of digital mask projection lithography can be effectively improved.
Example 2
The embodiment provides a specific implementation process of a digital mask projection lithography optimization method.
The parameters used for the simulation were first determined using an on-axis point source of light that emits polarized light in the x-direction. The system selects a wavelength of 343nm, a numerical aperture of 1.45 on an image side, a refractive index of 1 on an object side and a refractive index of 1.516 on an image side, adopts 100 x fine shrinkage, the period of a spatial light modulator used for simulation is 3.75 micrometers, the filling rate is 89 percent, and the simulation considers the filling rate to be a hundred percent for convenience (the simulation considers that the filling rate generally influences the absolute intensity of light intensity but does not influence the relative distribution of the light intensity).
Each pixel x and y dimension of the spatial light modulator is sampled at 10 points, so the object space is sampled at 375nm, corresponding to a 3.75nm sampling space at the image space. The simulation area selects the number of pixels of 31×31, namely the area corresponding to the image space 1162.5nm×1162.5 nm.
As shown in fig. 3 to 5, the amplitude diagrams of the point spread functions of the point light source vector imaging of the present embodiment polarized in the x, y, and z directions of the image plane are shown.
In order to conveniently evaluate the optimization effect of the digital mask inversion calculation lithography technology, the embodiment has the following evaluation criteria:
defining a graphic error:
defining normalized graphic errors:l is the total number of pixels at the edge of the lithographic pattern;
define feature size error (CDE): the dimensional error of the photoetching pattern at the measuring position;
placement error (PLE): the distance the lithographic pattern moves at the center point of the measurement location.
In the implementation process, as shown in fig. 6, an optimization schematic diagram of L-shaped lithography patterns and digital mask projection lithography is shown. The L-shaped pattern in fig. 6 (a) is a target pattern, the feature size is 112.5nm, fig. 6 (b) is a digital mask with an initial iteration value, fig. 6 (c) is a photoresist pattern corresponding to the digital mask with an initial iteration value, and fig. 6 (d) is an addition of the edges of the photoresist pattern corresponding to the digital mask with an initial iteration value and the edges of an ideal pattern. The digital mask with the iteration initial value is evaluated by adopting the evaluation standard, the PE value of the photoetching pattern generated by the non-optimized digital mask is 1600, the NPE is 2.76, and CDE and PLE are generated at more positions.
Fig. 6 (e) shows a digital mask with only amplitude graying and fixed phase after optimization by the digital mask projection lithography optimization method according to the present embodiment, fig. 6 (f) shows a photoresist pattern corresponding to the digital mask of (e), and fig. 6 (g) shows addition of edges of the photoresist pattern corresponding to the optimized digital mask and edges of an ideal pattern. The optimized digital mask produced a lithographic pattern with a PE value of 96 and an NPE of 0.165. But also the edges of the pattern are substantially coincident with the desired photolithographic pattern, except for some errors created by the corners of the pattern. Wherein the parameter is a r ＝100，I r =0.4, other parameters are consistent with those described above.
FIG. 7 is a schematic diagram of a grating pattern and its digital mask projection lithography optimization. FIG. 7 (a) is a grating pattern, which has a feature size of 112.5nm and a period of 255nm. Because the period of the target pattern is not an integer multiple of the digital mask pixels, the lithographic pattern cannot be generated without inversion calculation. Fig. 7 (b) is a digital mask for iterative initial values. Fig. 7 (c) shows the photoresist pattern corresponding to the digital mask of the iteration initial value, and fig. 7 (d) shows the addition of the edge of the photoresist pattern corresponding to the digital mask of the iteration initial value and the edge of the ideal pattern. The lithographic pattern produced by the non-optimized digital mask was evaluated using the above evaluation criteria, with a PE value of 7472 and NPE of 12.88, and CDE and PLE were produced at a greater number of locations.
Fig. 7 (e) shows a digital mask with only amplitude graying and fixed phase after optimization by the digital mask projection lithography optimization method according to the present embodiment, fig. 7 (f) shows a photoresist pattern corresponding to the digital mask of fig. 7 (e), and fig. 7 (g) shows addition of edges of the photoresist pattern corresponding to the optimized digital mask and edges of an ideal pattern. Wherein the optimized digital mask produces a lithographic pattern with a PE value of 301 and an NPE of 0.237. And the edges substantially coincide with the desired photolithographic pattern except for corners that are subject to some errors. Wherein the parameter is a r ＝100，I r =0.5, other parameters are consistent with those described above.
FIG. 8 is a schematic diagram of a typical lithographic pattern and its digital mask projection lithography optimization. Wherein, fig. 8 (a) is a typical photolithography pattern, the feature size is 112.5nm, fig. 8 (b) is a digital mask with an iteration initial value, fig. 8 (c) is a photoresist pattern corresponding to the digital mask with an iteration initial value, and fig. 8 (d) is an addition of the edge of the photoresist pattern corresponding to the digital mask with an iteration initial value and the edge of an ideal pattern. The lithographic pattern produced by the non-optimized digital mask was evaluated using the above evaluation criteria, with a PE value of 2052 and NPE of 2.56, and CDE and PLE were produced at a greater number of locations.
Fig. 8 (e) shows a digital mask with only amplitude graying and fixed phase after optimization by the digital mask projection lithography optimization method according to the present embodiment, fig. 8 (f) shows a photoresist pattern corresponding to the digital mask of fig. 8 (e), and fig. 8 (g) shows addition of edges of the photoresist pattern corresponding to the optimized digital mask and edges of an ideal pattern. The optimized digital mask produced a lithographic pattern with a PE value of 305 and an NPE of 0.38.
Fig. 8 (h) is a digital mask with amplitude graying and phase at 0 or pi after optimization of the gradient algorithm, fig. 8 (i) is a photoresist pattern corresponding to the digital mask of fig. 8 (h), and fig. 8 (j) is an addition of edges of the photoresist pattern corresponding to the optimized digital mask and edges of an ideal pattern. The optimized digital mask produces a lithographic pattern with a PE value of 121 and an NPE of 0.15, which has less pattern errors and improved rounded corners that are difficult to optimize relative to pure amplitude optimization. Wherein the parameter is a r ＝100，I r =0.4, other parameters are consistent with those described above.
As shown in FIG. 9, another exemplary lithographic pattern and its digital mask projection lithography optimization schematic are shown. Fig. 9 (a) is a typical photolithography pattern, wherein the feature size is 112.5nm, fig. 9 (b) is a digital mask with an iteration initial value, fig. 9 (c) is a photoresist pattern corresponding to the digital mask with an iteration initial value, and fig. 9 (d) is an addition of the edges of the photoresist pattern corresponding to the digital mask with an iteration initial value and the edges of an ideal pattern. The lithographic pattern produced by the non-optimized digital mask was evaluated using the above evaluation criteria, with a PE value of 2952 and NPE of 4.47, and CDE and PLE were produced at a greater number of locations.
Fig. 9 (e) shows a digital mask with only amplitude graying and fixed phase after optimization by the digital mask projection lithography optimization method according to the present embodiment, fig. 9 (f) shows a photoresist pattern corresponding to the digital mask of fig. 9 (e), and fig. 9 (g) shows addition of edges of the photoresist pattern corresponding to the optimized digital mask and edges of an ideal pattern. The optimized digital mask produced a lithographic pattern with a PE value of 275 and an NPE of 0.416. Fig. 9 (h) shows the optimized digital mask with amplitude graying and phase at 0 or pi, fig. 9 (i) shows the photoresist pattern corresponding to the digital mask of fig. 9 (h), and fig. 9 (j) shows the addition of the edges of the photoresist pattern corresponding to the optimized digital mask and the edges of the ideal pattern. The optimized digital mask produced a lithographic pattern with a PE value of 209, npe of 0.316, a pattern error smaller than that of pure amplitude optimization,some of its difficult-to-optimize rounded corners are also improved. Wherein the parameter is a r ＝100，I r =0.5, other parameters are consistent with those described above.
As shown in FIG. 10, another exemplary lithographic pattern and its digital mask projection lithography optimization schematic are shown. FIG. 10 (a) is a typical lithographic pattern with a feature size of 37.5nm and a period of 150nm, and with an initial iteration set as an alternating inverse mask, which, due to its characteristics, has a resolvable period half that of a conventional binary mask; fig. 10 (b) is a digital mask of an iteration initial value, fig. 10 (c) is a photoresist pattern corresponding to the digital mask of the iteration initial value, and fig. 10 (d) is an addition of an edge of the photoresist pattern corresponding to the digital mask of the iteration initial value and an edge of an ideal pattern. The lithographic pattern produced by the non-optimized digital mask was evaluated using the above evaluation criteria, with a PE value of 7500 and NPE of 4.68, and CDE and PLE were produced at a greater number of locations.
Fig. 10 (e) shows a digital mask with only amplitude graying and fixed phase after optimization by the digital mask projection lithography optimization method according to the present embodiment. Fig. 10 (f) shows the photoresist pattern corresponding to the digital mask of fig. 10 (e), and fig. 10 (g) shows the addition of the edges of the photoresist pattern corresponding to the optimized digital mask and the edges of the ideal pattern. The optimized digital mask produced a lithographic pattern with a PE value of 186 and an NPE of 0.116. Wherein the parameter is a r ＝100，I r =0.25, other parameters are consistent with those described above.
Example 3
The present embodiment provides a digital mask projection lithography optimization system, and the digital mask projection lithography optimization method provided in embodiment 1 is applied. FIG. 11 is a schematic diagram showing the structure of the digital mask projection lithography optimizing system according to the present embodiment.
The digital mask projection lithography optimization system of the present embodiment includes an on-axis point light source 1, a spatial light modulator 2, a processor 3, wherein: the processor 3 performs the steps of the digital mask projection lithography optimization method of embodiment 1; the on-axis point light source 1 is loaded on the spatial light modulator 2 after generating an optimized digital mask M by the processor 3,after the incident light output by the on-axis point light source 1 is modulated by the spatial light modulator 2, photoetching is carried out on photoresist to obtain a target patternThe lithographic pattern Z with the smallest gap.
The digital mask M in this embodiment is composed of a programmable pure amplitude spatial light modulator 2 (Amplitude LCoS SLM), a programmable pure Phase spatial light modulator 2 (Phase LCoS SLM). Wherein the spatial light modulator 2 is composed of an array of individually addressable and controllable pixels, each of which performs complex amplitude modulation of transmitted light, reflected light, including modulation of phase, intensity or switching state.
Further, in combination with a digital micromirror array (DMD), arbitrary modulations of phase and amplitude are achieved.
The processor 3 in this embodiment is configured to execute a processing according to a target patternCarrying out digital mask inversion calculation on a preset digital mask projection lithography imaging model, carrying out iterative optimization on the digital mask projection lithography imaging model based on a steepest descent method to obtain a digital mask M, and then carrying out programming control on a spatial light modulator 2 to obtain a target pattern +.>The lithographic pattern Z with the smallest gap.
The same or similar reference numerals correspond to the same or similar components;
the terms describing the positional relationship in the drawings are merely illustrative, and are not to be construed as limiting the present patent;
it is to be understood that the above examples of the present invention are provided by way of illustration only and not by way of limitation of the embodiments of the present invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are desired to be protected by the following claims.
Claims (6)
1. A digital mask projection lithography optimization method, comprising the steps of:
establishing a matrix expression of complex amplitude distribution of the digital mask, and constructing a digital mask projection lithography imaging model; the digital mask projection lithography imaging model comprises an optical model and a chemical model of photoresist;
the digital mask is generated by an amplitude spatial light modulator, and the complex amplitude transmittance m (x, y) of the digital mask is expressed as:
wherein a is m,n (x-md x ,y-nd y ) Representing the light field modulation at the pixel point (m, n), and the amplitude of the light field modulation is any real number from 0 to 1 after normalization, and the phase is 0 or pi; u (x-md) x ,y-nd y ) The complex amplitude transmittance on the pixel points (m, n) is represented, and the u function is a rectangular function; d, d x 、d y Respectively representing the period in the x direction and the period in the y direction of the pixel arrangement;
when the matrix expression of the complex amplitude distribution with the digital mask is established, the expression is:
in the method, in the process of the invention,in the form of a discrete matrix of complex amplitude transmittance m (x, y) of a digital mask, +.>Is a as m,n (x-md x ,y-nd y ) Matrix expression form, core is u (x-md) x ,y-nd y ) Representing a sampling matrix for individual pixels of the digital mask; />Represents the kronecker product;
then an optical model of the digital mask projection lithography imaging model is established by using the discrete matrix of the digital mask complex amplitude transmittance, and the expression formula is as follows:
the generated lithographic pattern Z is expressed as:
wherein T { M } represents a lithography forward system, and represents a lithography pattern obtained by receiving the digital mask M; h is a p Representing the point spread functions in the x, y, z polarization directions;
establishing a cost function F with respect to graphic fidelity by taking a digital mask as a variable;
given binary target graphicsPerforming digital mask inversion calculation on the digital mask projection lithography imaging model, calculating the gradient of the digital mask based on the cost function F, and performing iterative optimization on the digital mask projection lithography imaging model to obtain a digital mask M; wherein:
in the digital mask inversion calculation process, for a given binary target patternFind a digital mask->And is loaded in spaceEnabling the photoetching pattern Z epsilon R on the light modulator N×N Is +.>The difference between (2) is the smallest, and the cost function F is expressed as:
wherein N is M The number of pixels arranged in a certain direction for the digital mask;representing the square of the F-norm;
loading the digital mask M on a spatial light modulator to obtain a pattern corresponding to the target patternThe lithographic pattern Z with the smallest gap.
2. The digital mask projection lithography optimization method of claim 1, wherein the chemical model of the photoresist is expressed as:
wherein a is r The larger the value of the constant coefficient is, the closer the sigmoid function is to the hard threshold function; t is t r Is a photoresist threshold; z (x, y) has a value between 0 and 1; i (x, y) represents a light source imaging model, and the expression formula is as follows:
in the formula, h p (x, y) represents the point spread function in the x, y, z polarization directions, and m (x, y) represents the complex amplitude transmittance of the digital mask; * Representing a convolution operation.
3. The digital mask projection lithography optimization method according to claim 2, wherein the light source imaging model I (x, y) comprises a linear superposition of coherent system light intensities in polarization directions.
4. The method according to claim 1, wherein in the digital mask inversion calculation, when the digital mask is only loaded with gray scale amplitude and the phase is not modulated, the pixel M of the ith row and jth column of the digital mask M i,j ∈[0,1]Wherein i, j=1, 2, N M There is an optimization problem:
when the digital mask is loaded with gray amplitude and its bit is 0 or pi, the pixel M of the ith row and jth column of the digital mask M i,j ∈[-1,1]Wherein i, j=1, 2, N M There is an optimization problem:
M i,j ＝cosθ i,j
wherein θ i,j ∈[-∞,+∞]The method comprises the steps of carrying out a first treatment on the surface of the In θ i,j Pixels M representing the ith row and jth column of the digital mask M i,j Corresponding discrete matrix elements.
5. The method according to claim 4, wherein in optimizing the digital mask projection lithography imaging model, a steepest descent method is used to calculate a gradient of the cost function F to the digital mask according to the optimization problem.
6. A digital mask projection lithography optimization system for use in a digital mask projection lithography optimization method according to any one of claims 1-5, comprising an on-axis point light source, a spatial light modulator, a processor, wherein:
the processor performs the steps of the digital mask projection lithography optimization method of any one of claims 1-5;
the on-axis point light source generates an optimized digital mask M through the processor and then loads the optimized digital mask M on the spatial light modulator to obtain a target graphThe lithographic pattern Z with the smallest gap.
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