CN113495435A - Digital mask projection lithography optimization method and system - Google Patents

Digital mask projection lithography optimization method and system Download PDF

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CN113495435A
CN113495435A CN202110580510.0A CN202110580510A CN113495435A CN 113495435 A CN113495435 A CN 113495435A CN 202110580510 A CN202110580510 A CN 202110580510A CN 113495435 A CN113495435 A CN 113495435A
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digital mask
projection lithography
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pattern
mask
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CN113495435B (en
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段宣明
陈经涛
赵圆圆
朱建新
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Jinan University
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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
    • 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
    • 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
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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Abstract

The invention provides a digital mask projection lithography optimization method and a system for solving the problems that the actual lithography pattern deviates from the target design pattern and the lithography resolution is difficult to improve in the digital mask projection lithography, wherein the method comprises the following steps: establishing a matrix expression of complex amplitude distribution of a digital mask, and constructing a digital mask projection lithography imaging model; establishing a cost function F about the fidelity of the graph with a digital mask as a variable; given a binary object pattern
Figure DDA0003085877640000011
Performing 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 iterating for a certain number of times or meeting a certain condition to obtain a digital mask M; loading the digital mask M on a spatial light modulator to obtain a target pattern
Figure DDA0003085877640000012
The smallest difference lithographic pattern Z.

Description

Digital mask projection lithography optimization method and system
Technical Field
The invention relates to the technical field of digital mask projection lithography, in particular to a layout optimization method and system of digital mask projection lithography.
Background
As lithographic feature sizes decrease, the lithographic pattern will be severely distorted, so Inverse Lithography (ILT) is typically employed in conventional mask Lithography to address image distortion and improve lithographic pattern resolution. The traditional photoetching mostly adopts inversion calculation mask optimization and correction based on pixel representation, the essence is to optimize the complex amplitude transmittance of each sampled pixel point, the graphs optimized by the method are all complex topological structures, the manufacturing difficulty and the cost of the mask are increased, and certain graphs cannot be manufactured. Commercial inverse lithography software constrains the manufacturing rules of the mask to ensure that it optimizes mask manufacturability, but this again can have unpredictable effects on the optimized mask, such as feature size errors, pattern placement errors, etc.
In the current 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 digitalized mask cost is far lower than that of the traditional solid mask manufactured based on 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, the flexibility and the production efficiency of the photoetching pattern, so the technology is widely concerned by the application fields of small-batch and customized production in the industry, national defense and the like. However, as the feature size of maskless projection lithography is reduced, the lithographic pattern still deviates significantly from the designed pattern, or the resolution of digital mask projection lithography is low. Therefore, the digital mask needs to be subjected to proximity effect correction based on inverse lithography, but the traditional mask inversion calculation lithography algorithm cannot be directly applied to optimization of the discretized digital mask.
Disclosure of Invention
The invention provides a digital mask projection lithography optimization method and a digital mask projection lithography optimization system for solving the problems that the actual lithography pattern deviates from the target design pattern and the lithography resolution is difficult to improve in the existing digital mask projection lithography.
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 a digital mask, and constructing a digital mask projection lithography imaging model;
establishing a cost function F about the fidelity of the graph with a digital mask as a variable;
given a binary object pattern
Figure BDA0003085877620000025
Performing 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;
loading the digital mask M on a spatial light modulator to obtain a target pattern
Figure BDA0003085877620000024
The smallest difference lithographic pattern Z.
In the technical scheme, the method comprises the following steps of,
preferably, the digital mask projection lithography imaging model includes an optical model and a chemical model of the photoresist.
Preferably, the chemical model of the photoresist is represented as:
Figure BDA0003085877620000021
in the formula, arThe coefficient is a constant coefficient, and the larger the value of the coefficient is, the closer the sigmoid function is to the hard threshold function; t is trIs the photoresist threshold; the value of Z (x, y) is between 0 and 1; i (x, y) represents a light source imaging model, and the expression formula is as follows:
Figure BDA0003085877620000022
in the formula, hp(x, y) represents a point spread function in the x, y, z polarization directions, and m (x, y) represents the complex amplitude transmittance of the digital mask; denotes convolution operation.
Preferably, the light source imaging model I (x, y) comprises a linear superposition of the coherent system light intensities in the polarization directions.
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 represented by:
Figure BDA0003085877620000023
in the formula, am，n(x-mdx，y-ndy) Representing the light field modulation on the pixel point (m, n), and after normalization, the amplitude of the light field modulation is any real number from 0 to 1, and the phase is 0 or pi; u (x-md)x，y-ndy) Representing complex amplitude transmittance on pixel points (m, n), wherein the u function is a rectangular function; dx、dyRespectively showing the x-direction period and the y-direction period of the pixel arrangement;
when the matrix expression of the complex amplitude distribution of the digital mask is established, the expression is as follows:
Figure BDA0003085877620000031
wherein M is a discrete matrix form of complex amplitude transmittance M (x, y) of the digital mask, and M is am，n(x-mdx，y-ndy) The core is u (x-md)x，y-ndy) A discrete representation of (a) representing a sampling matrix for a single pixel of the digital mask;
Figure BDA0003085877620000032
representing the kronecker product.
Preferably, an optical model of the digital mask projection lithography imaging model is established by using the discrete matrix of the complex amplitude transmittance of the digital mask, and the expression formula is as follows:
Figure BDA0003085877620000033
the resulting lithographic pattern Z is then expressed as:
Figure BDA0003085877620000034
in the formula, T { M } represents a lithography forward system, and represents a lithography pattern obtained by receiving the digital mask M.
Preferably, the digital mask inversion calculation process is performed for a given binary target pattern
Figure BDA0003085877620000035
Finding a digital mask
Figure BDA0003085877620000036
And loaded on a spatial light modulator to enable lithographic patterning
Figure BDA0003085877620000037
And the target pattern
Figure BDA0003085877620000038
With the smallest distance, the cost function F is expressed as:
Figure BDA0003085877620000039
in the formula, NMRepresenting the number of pixels of the digital mask pixels arranged in the x or y direction;
Figure BDA00030858776200000310
representing the square of the F-norm.
Preferably, the digital mask inversion calculationIn the process, when the digital mask only loads gray amplitude and does not modulate the phase, the pixel M of the ith row and the jth column of the digital mask Mi，j∈[0，1]Wherein i, j is 1, 2MThen there is an optimization problem:
Figure BDA00030858776200000311
wherein,
Figure BDA00030858776200000312
θi，j∈[-∞，+∞]；
when the digital mask is loaded with gray scale amplitude and the phase thereof is 0 or pi, the element M of the ith row and the jth column of the digital mask Mi，j∈[-1，1]Wherein i, j is 1, 2MThen there is an optimization problem:
M＝cosθ
wherein,
Figure BDA00030858776200000313
θi，j∈[-∞，+∞](ii) a Wherein theta denotes a digital mask, thetai，jRepresenting the elements in the ith row and jth column of the digital mask theta.
As a preferable scheme, in the optimization process of the digital mask projection lithography imaging model, according to the optimization problem, the gradient of the cost function F to the digital mask is calculated by adopting a steepest descent method.
A digital mask projection lithography optimization system is applied to the digital mask projection lithography optimization method of any one of the 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 solutions; the on-axis point light source generates an optimized digital mask M through the processor and then loads the digital mask M on the spatial light modulator to obtain a target pattern
Figure BDA0003085877620000043
The smallest difference lithographic pattern Z.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that: the invention uses the spatial light modulator to realize the 'digital mask', replaces the expensive mask of the traditional photoetching system, constructs a digital mask projection photoetching imaging model aiming at the digital mask, and further adopts the digital mask inversion calculation photoetching technology to solve the complex amplitude modulation coefficient loaded by each pixel of the digital mask (namely to solve one digital mask) so as to lead the corresponding photoetching pattern Z and the expected target pattern Z to be
Figure BDA0003085877620000042
And the resolution of the digital mask projection lithography can be effectively improved.
Drawings
FIG. 1 is a flowchart of a digital mask projection lithography optimization method of example 1.
FIG. 2 is a drawing showing a structure of example 1
Figure BDA0003085877620000041
Schematic diagram of the operation.
FIG. 3 is a graph showing the amplitude of the point spread function for x-direction polarization of a point light source of example 1.
FIG. 4 is a graph showing the amplitude of the point spread function for 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 for z-direction polarization of a point light source of example 1.
FIG. 6 is a schematic diagram of the optimization of the L-shaped lithographic pattern and its digital mask projection lithography in example 2.
Fig. 7 is a schematic diagram of grating type lithography patterns and their digital mask projection lithography optimization of embodiment 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 a schematic diagram of another exemplary lithographic pattern and its digital mask projection lithography optimization of example 2.
FIG. 10 is a schematic diagram of another exemplary lithographic pattern and its digital mask projection lithography optimization of example 2.
FIG. 11 is a schematic structural diagram of a digital mask projection lithography optimizing system of embodiment 3.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
The present embodiment provides a method for optimizing digital mask projection lithography, and as shown in fig. 1, the method is a flowchart of the method for optimizing digital mask projection lithography according to the present embodiment.
The digital mask projection lithography optimization method provided by the embodiment comprises the following steps:
step 1: and establishing a matrix expression of the complex amplitude distribution of the digital mask, and constructing a digital mask projection lithography imaging model.
In the embodiment where the digital mask is generated by a spatial light modulator, the complex amplitude transmittance m (x, y) of the digital mask is represented as:
Figure BDA0003085877620000051
in the formula, am，n(x-mdx，y-ndy) Representing the light field modulation on the pixel point (m, n), and after normalization, the amplitude of the light field modulation is any real number from 0 to 1, and the phase is 0 or pi; dx、dyRespectively representing the pixel periods in the x and y directions; u (x-md)x，y-ndy) The complex amplitude transmittance at pixel points (m, n) is represented, and the u function is a rectangular function since the spatial light modulator is generally composed of rectangular small pixel elements which are periodically arranged.
Therefore, in the step of establishing the matrix expression of the complex amplitude distribution by using the digital mask, the expression is as follows:
Figure BDA0003085877620000052
wherein M is a discrete matrix form of complex amplitude transmittance M (x, y) of the digital mask, and M is am，n(x-mdx，y-ndy) The core is u (x-md)x，y-ndy) A discrete representation of (a) representing a sampling matrix for a single pixel of the digital mask;
Figure BDA0003085877620000053
representing the Kronecker Product (Kronecker Product).
In this embodiment, in consideration of the particularity of the digital mask, complex amplitude transmittances of the digital mask to lights in different directions may be different, that is, the effectiveness of the illumination mode of the conventional mask in off-axis illumination cannot be verified, so that in order to ensure the normal operation of the spatial light modulator, the illumination mode using an on-axis point light source is represented as follows:
Figure BDA0003085877620000054
in the formula, hp(x, y) represents a point spread function in the x, y, z polarization directions, and m (x, y) represents the complex amplitude transmittance of the digital mask; denotes convolution operation. In addition, the light source imaging model I (x, y) in this embodiment is a linear superposition of the coherent system light intensities in the 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.
Wherein, for the chemical model of the photoresist, when the received light intensity of the photoresist (in this embodiment, a negative photoresist is taken as an example) reaches the exposure threshold, the photoresist molecules are crosslinked and are insoluble in the developing solution, and the crosslinked photoresist molecules are retained as the photoresist pattern; the hard threshold model is:
Figure BDA0003085877620000061
in the formula, ZbIs represented byrIs the photoresist threshold; from the above formula, ZbIn the inversion calculation lithography technology, in order to make the cost function derivable, the sigmoid function is used in the present embodiment instead of the hard threshold function, and then the chemical model of the photoresist in the present embodiment is expressed as:
Figure BDA0003085877620000062
in the formula, arThe coefficient is a constant coefficient, and the larger the value of the coefficient is, the closer the sigmoid function is to the hard threshold function; t is trIs the photoresist threshold; the value of Z (x, y) is between 0 and 1. The significance of the function is that if the received light intensity of a certain pixel point is greater than the threshold t of the photoresistrThe closer its value is to 1, the more it represents the position exposure; if the received light intensity of a certain pixel point is less than the photoresist threshold trThe closer its value is to 0, the more it represents that the position is not exposed.
In this embodiment, an optical model of a digital mask projection lithography imaging model is established by using a discrete matrix of complex amplitude transmittance of a digital mask, and an expression formula thereof is as follows:
Figure BDA0003085877620000063
the resulting lithographic pattern Z is then expressed as:
Figure BDA0003085877620000064
in the formula, T { M } represents a lithography forward system, and represents a lithography pattern obtained by receiving the digital mask M.
Step 2: a cost function F is established with respect to the fidelity of the pattern, using the digital mask as a variable.
In the digital mask inversion calculation process of the present embodiment, for a given binary target pattern
Figure BDA0003085877620000065
Finding a digital mask
Figure BDA0003085877620000066
And loaded on the spatial light modulator to make the photoetching pattern Z epsilon RN×NAnd the target pattern
Figure BDA0003085877620000067
With the smallest gap, the cost function F is expressed as:
Figure BDA0003085877620000071
in the formula, NMRepresenting the number of pixels arranged in the x or y direction of the digital mask;
Figure BDA0003085877620000072
the square of the F norm is expressed, in which the lithographic pattern Z and the target pattern are expressed
Figure BDA0003085877620000073
Square of the euler distance of (d). The cost function F takes the digital mask M as a variable, so that the cost function F represents the photoetching pattern Z and the target pattern obtained by the digital mask M
Figure BDA0003085877620000074
The smaller the difference, the closer the resulting lithographic pattern Z is to the target pattern
Figure BDA0003085877620000075
And step 3: given a binary object pattern
Figure BDA0003085877620000076
And modeling the digital mask projection lithography imageAnd performing inversion calculation on the digital mask, 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 iterating for a certain number of times or meeting a certain condition to obtain the digital mask M.
In this embodiment, when the digital mask is loaded with only gray scale amplitude and does not modulate the phase, the element M in the ith row and the jth column in the digital mask Mi，j∈[0，1]Wherein i, j is 1, 2MFor the difficulty of solving constrained optimization, the present embodiment transforms the problem into an unconstrained optimization problem by using trigonometric functions:
Figure BDA0003085877620000077
wherein,
Figure BDA0003085877620000078
θi，j∈[-∞，+∞]，i，j＝1，2，...，NM(ii) a Wherein theta denotes a digital mask, thetai，jA digital mask discrete matrix element representing an ith row and a jth column;
and calculating the gradient of the cost function F to the digital mask M by adopting a steepest descent method, namely calculating the gradient of the cost function F to the digital mask theta:
Figure BDA0003085877620000079
when the digital mask is loaded with gray scale amplitude and the phase thereof is 0 or pi, the element M of the ith row and the jth column in the digital mask Mi，j∈[-1，1]Wherein i, j is 1, 2MFor the difficulty of solving constrained optimization, the present embodiment transforms the problem into an unconstrained optimization problem by using trigonometric functions:
M＝cosθ
wherein,
Figure BDA00030858776200000710
θi，j∈[-∞，+∞]，i，j＝1，2，...，NM(ii) a And calculating the gradient of the cost function F to the digital mask M by adopting a steepest descent method, namely calculating the gradient of the cost function F to the digital mask theta:
Figure BDA00030858776200000711
in the formula, arParameters representing sigmoid functions; re {. is used for representing a real part;
Figure BDA00030858776200000712
a matrix h of representation pairspTurning the upper part, the lower part, the left part and the right part; h isp *A matrix h of representation pairspThe conjugate taking operation; o represents the corresponding multiplication of matrix elements; core represents a core matrix; t represents a target photoetching pattern;
Figure BDA0003085877620000081
the operation defined by the embodiment is that the sampling points in each pixel are multiplied by the matrix elements in the core matrix (sampling matrix of single pixel of digital mask) correspondingly and then added, and a new matrix is formed according to the original arrangement sequence; if the core matrix is a full 1 matrix, the operation is equal to average pooling, and since the kronecker product with the full 1 matrix is equal to an upsampling process, the gradient calculation should be a downsampling process.
As shown in FIG. 2, it is the same as that of the present embodiment
Figure BDA0003085877620000082
Schematic diagram of the operation. The core matrix represented by 3 × 3 in the figure is performed with the matrix represented by 6 × 6
Figure BDA0003085877620000083
In operation, assuming that the 6 × 6 matrix is the gradient of each sample point of the digital mask with respect to F, the sample points of the same color are from the same digital mask pixel, and the amplitude spatial light characteristic can only be adjustedThe amplitude of each individual pixel cannot be modulated at different positions within the pixel, so the values of the sampling points from the same digital mask pixel must also be kept consistent. This example adopts
Figure BDA0003085877620000084
The operation keeps the sampling points consistent during the iteration within an "area" of one pixel size of the digital mask.
Further, the present embodiment calculates the gradient of the cost function F to the digital mask by using the steepest descent method. The steepest descent method generally directly uses the reverse direction of the gradient as an iteration direction, and uses accurate search or non-accurate line search as a step length or a constant step length; in this embodiment, the value of the digital mask is continuously iterated by using a steepest descent method, the digital mask projection lithography imaging model is optimized, and iteration is stopped after a certain number of iterations or a certain condition is satisfied, so as to obtain the digital mask M.
And 4, step 4: loading the digital mask M on a spatial light modulator to obtain a target pattern
Figure BDA0003085877620000086
The smallest difference lithographic pattern Z.
The digital mask projection lithography optimization method provided in this embodiment uses the spatial light modulator to realize a "digital mask", replaces an expensive mask of a conventional lithography system, constructs a digital mask projection lithography imaging model for the digital mask, and further solves a complex amplitude modulation coefficient loaded by each pixel of the digital mask (i.e., solves one digital mask) by using a digital mask inversion computation lithography technology, so that a corresponding lithography pattern Z and an expected target pattern Z are obtained
Figure BDA0003085877620000085
And the resolution of the 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.
Firstly, parameters used for simulation are determined, and an on-axis point light source is adopted for illumination, wherein the point light source emits polarized light in the x direction. The system has the selected wavelength of 343nm, the image-side numerical aperture of 1.45, the object-side refractive index of 1 and the image-side refractive index of 1.516, the system adopts 100 x fine reduction, the period of a spatial light modulator used for simulation is 3.75 microns, the filling rate is 89 percent, and the filling rate is considered to be hundred percent for the simulation convenience (considering that the filling rate generally influences the absolute intensity of light intensity and does not influence the relative distribution of the light intensity).
10 points are sampled in each pixel x and y dimension of the spatial light modulator, so the object side sampling interval is 375nm, corresponding to a sampling interval of 3.75nm for the image side. The simulation area adopts the number of 31 multiplied by 31 pixels, namely the area corresponding to the image side 1162.5nm multiplied by 1162.5 nm.
As shown in fig. 3 to 5, they are schematic amplitude diagrams of point spread functions of the point light source vector imaging in x, y, and z directions of the image plane.
In this embodiment, in order to evaluate the optimization effect of the digital mask inversion calculation lithography technology, the following evaluation criteria are provided:
defining a pattern error:
Figure BDA0003085877620000091
defining a normalized graphic error:
Figure BDA0003085877620000092
l is the total number of pixels at the edge of the photoetching pattern;
define feature size error (CDE): the scale error of the photoetching pattern at the measuring position;
placement error (PLE): the distance the center point of the lithography pattern moves at the measurement location.
In the specific implementation, as shown in fig. 6, a schematic diagram of an L-shaped lithography pattern and its digital mask projection lithography optimization is shown. The L-shaped resist pattern in fig. 6(a) is a target pattern having a characteristic dimension of 112.5nm, fig. 6(b) is an iteration initial digital mask, fig. 6(c) is a resist pattern corresponding to the iteration initial digital mask, and fig. 6(d) is a sum of the edge of the resist pattern corresponding to the iteration initial digital mask and the edge of an ideal pattern. The evaluation criteria described above were used to evaluate the initial iteration of the digital mask, and the unaptimized digital mask produced a lithographic pattern with a PE of 1600, an NPE of 2.76, and a greater number of locations for CDE and PLE.
Fig. 6(e) is a digital mask with only amplitude graying and fixed phase optimized by the digital mask projection lithography optimization method proposed in this embodiment, fig. 6(f) is a photoresist pattern corresponding to the digital mask of (e), and fig. 6(g) is a sum of an edge of the photoresist pattern corresponding to the optimized digital mask and an edge of an ideal pattern. The optimized digital mask produced a lithographic pattern with a PE value of 96 and an NPE of 0.165. And its edge substantially coincides with the desired lithographic pattern, except for some errors due to pattern corners. Wherein the parameter is ar＝100，IrOther parameters are consistent with those described above, 0.4.
Fig. 7 shows a schematic diagram of optimization of grating-type lithography and its digital mask projection lithography. FIG. 7(a) is a grating-type lithographic pattern with a feature size of 112.5nm and a period of 255 nm. Because the period of the target pattern is not integral multiple of the pixel of the digital mask, the photoetching pattern cannot be generated without the inverse calculation photoetching technology. FIG. 7(b) is a digital mask of the initial values of the iteration. Fig. 7(c) shows a photoresist pattern corresponding to the initial iteration value digital mask, and fig. 7(d) shows the sum of the edge of the photoresist pattern corresponding to the initial iteration value digital mask and the edge of the ideal pattern. The evaluation of the lithographic patterns produced by the digital mask without optimization was carried out using the above evaluation criteria, with a PE value of 7472, an NPE of 12.88, and the production of CDE and PLE in more locations.
Fig. 7(e) is a digital mask with only amplitude graying and fixed phase optimized by the digital mask projection lithography optimization method proposed in this embodiment, fig. 7(f) is a photoresist pattern corresponding to the digital mask of fig. 7(e), and fig. 7(g) is a sum of an edge of the photoresist pattern corresponding to the optimized digital mask and an edge of an ideal pattern. Wherein the optimized digital mask produces a lithographic pattern having a PE value of 301 and an NPE value of 0.237. And in addition to the cornersAfter some errors have occurred, the edges substantially coincide with the lithographic pattern we desire. Wherein the parameter is ar＝100，IrOther parameters were consistent with those described above, 0.5.
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 lithography pattern with a feature size of 112.5nm, fig. 8(b) is a digital mask of an initial iteration value, fig. 8(c) is a photoresist pattern corresponding to the digital mask of the initial iteration value, and fig. 8(d) is a sum of an edge of the photoresist pattern corresponding to the digital mask of the initial iteration value and an edge of an ideal pattern. The evaluation of the lithographic patterns produced by the digital mask without optimization was carried out using the above evaluation criteria, with a PE value of 2052, an NPE of 2.56, and CDE and PLE produced in more locations.
Fig. 8(e) is a digital mask with only amplitude graying and fixed phase optimized by the digital mask projection lithography optimization method proposed in the present embodiment, fig. 8(f) is a photoresist pattern corresponding to the digital mask of fig. 8(e), and fig. 8(g) is a sum of an edge of the photoresist pattern corresponding to the optimized digital mask and an edge 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) shows a digital mask in which the phase is 0 or pi and the amplitude is grayed after the optimization by the gradient algorithm, fig. 8(i) shows a photoresist pattern corresponding to the digital mask of fig. 8(h), and fig. 8(j) shows the sum of the edge of the photoresist pattern corresponding to the optimized digital mask and the edge of the ideal pattern. The optimized digital mask produces a lithographic pattern with a PE of 121 and an NPE of 0.15, which has a smaller pattern error and improved rounded corners, which are difficult to optimize, relative to pure amplitude optimization. Wherein the parameter is ar＝100，IrOther parameters are consistent with those described above, 0.4.
FIG. 9 is a schematic diagram of another exemplary lithographic pattern and its digital mask projection lithography optimization. Fig. 9(a) shows a typical lithographic pattern with a feature size of 112.5nm, fig. 9(b) shows an iteration initial digital mask, fig. 9(c) shows a photoresist pattern corresponding to the iteration initial digital mask, and fig. 9(d) shows the sum of the edge of the photoresist pattern corresponding to the iteration initial digital mask and the edge of the ideal pattern. The evaluation of the lithographic patterns produced by the digital mask without optimization was carried out using the above evaluation criteria, with a PE value of 2952, an NPE of 4.47, and in more places CDE and PLE.
Fig. 9(e) is a digital mask with fixed phase and only amplitude graying optimized by the digital mask projection lithography optimization method proposed in the present embodiment, fig. 9(f) is a photoresist pattern corresponding to the digital mask of fig. 9(e), and fig. 9(g) is a sum of an edge of the photoresist pattern corresponding to the optimized digital mask and an edge 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) is a digital mask in which the optimized amplitude is grayed and the phase is 0 or pi, fig. 9(i) is a photoresist pattern corresponding to the digital mask of fig. 9(h), and fig. 9(j) is a sum of the edge of the photoresist pattern corresponding to the optimized digital mask and the edge of the ideal pattern. The optimized digital mask produces a lithographic pattern with a PE of 209 and an NPE of 0.316, which has a smaller pattern error and improved rounding compared to pure amplitude optimization, which is difficult to optimize. Wherein the parameter is ar＝100，IrOther parameters were consistent with those described above, 0.5.
FIG. 10 is a schematic diagram of another exemplary lithographic pattern and its digital mask projection lithography optimization. Wherein, fig. 10(a) is a typical lithography pattern, the characteristic dimension is 37.5nmnm, the period is 150nm, the iteration initial value is set as an alternate reverse mask, and the resolvable period of the alternate reverse mask is half of that of the traditional binary mask due to the characteristics of the alternate reverse mask; fig. 10(b) shows the digital mask of the initial iteration value, fig. 10(c) shows the photoresist pattern corresponding to the digital mask of the initial iteration value, and fig. 10(d) shows the sum of the edge of the photoresist pattern corresponding to the digital mask of the initial iteration value and the edge of the ideal pattern. The evaluation of the lithographic patterns produced by the digital mask without optimization was performed using the above evaluation criteria, with a PE value of 7500, an NPE of 4.68, and the production of CDE and PLE in more locations.
FIG. 10(e) is a graph showing amplitude-only graying after optimization by the digital mask projection lithography optimization method proposed in this embodimentA phase-fixed digital mask. Fig. 10(f) shows a photoresist pattern corresponding to the digital mask of fig. 10(e), and fig. 10(g) shows the sum of the edge of the photoresist pattern corresponding to the optimized digital mask and the edge 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 ar＝100，IrOther parameters are consistent with those described above, 0.25.
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 structural diagram of the digital mask projection lithography optimizing system of the present embodiment.
The digital mask projection lithography optimizing system of the embodiment comprises an on-axis point light source 1, a spatial light modulator 2 and a processor 3, wherein: the processor 3 executes the steps of the digital mask projection lithography optimization method of embodiment 1; the on-axis point light source 1 generates an optimized digital mask M through the processor 3 and then loads the digital mask M on the spatial light modulator 2, and incident light output by the on-axis point light source 1 is modulated by the spatial light modulator 2 and then is subjected to photoetching on photoresist to obtain a target pattern
Figure BDA0003085877620000121
The smallest difference lithographic pattern Z.
The digital mask M in this embodiment is composed of a programmable pure Amplitude spatial light modulator 2(Amplitude LCoS SLM) and a programmable Phase-only spatial light modulator 2 (Phase LCoS SLM). The spatial light modulator 2 is composed of an array of independently addressable and controllable pixels, each of which performs complex amplitude modulation on its transmitted light and reflected light, including modulation of phase, intensity or switching state.
Further, in combination with a digital micromirror array (DMD), arbitrary modulation of phase and amplitude is achieved.
The processor 3 in the present embodiment is used for processing the graphics according to the target
Figure BDA0003085877620000122
Performing digital mask inversion calculation on a preset digital mask projection photoetching imaging model, performing iterative optimization on the digital mask projection photoetching imaging model based on the steepest descent method to obtain a digital mask M, and performing programming control on the spatial light modulator 2 to obtain a target graph
Figure BDA0003085877620000123
The smallest difference lithographic pattern Z.
The same or similar reference numerals correspond to the same or similar parts;
the terms describing positional relationships in the drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (10)

1. A method for optimizing digital mask projection lithography, comprising the steps of:
establishing a matrix expression of complex amplitude distribution of a digital mask, and constructing a digital mask projection lithography imaging model;
establishing a cost function F about the fidelity of the graph with a digital mask as a variable;
given a binary object pattern
Figure FDA0003085877610000011
Performing 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;
loading the digital mask M on a spatial light modulator to obtain a target pattern
Figure FDA0003085877610000012
The smallest difference lithographic pattern Z.
2. The digital mask projection lithography optimization method according to claim 1, wherein the digital mask projection lithography imaging model comprises an optical model and a chemical model of the photoresist.
3. The digital mask projection lithography optimization method according to claim 2, wherein the chemical model of the photoresist is represented as:
Figure FDA0003085877610000013
in the formula, arThe coefficient is a constant coefficient, and the larger the value of the coefficient is, the closer the sigmoid function is to the hard threshold function; t is trIs the photoresist threshold; the value of Z (x, y) is between 0 and 1; i (x, y) represents a light source imaging model, and the expression formula is as follows:
Figure FDA0003085877610000014
in the formula, hp(x, y) represents a point spread function in the x, y, z polarization directions, and m (x, y) represents the complex amplitude transmittance of the digital mask; denotes convolution operation.
4. The digital mask projection lithography optimization method according to claim 3, wherein the light source imaging model I (x, y) comprises a linear superposition of the coherent system light intensities in the polarization directions.
5. The digital mask projection lithography optimization method according to claim 3, wherein said digital mask is generated by an amplitude spatial light modulator, said digital mask having a complex amplitude transmittance m (x, y) expressed as:
Figure FDA0003085877610000015
in the formula, am，n(x-mdx，y-ndy) Representing the light field modulation on the pixel point (m, n), and after normalization, the amplitude of the light field modulation is any real number from 0 to 1, and the phase is 0 or pi; u (x-md)x，y-ndy) Representing complex amplitude transmittance on pixel points (m, n), wherein the u function is a rectangular function; dx、dyRespectively indicating the period of the pixel arrangement in the x direction and the period in the y direction;
when the matrix expression of the complex amplitude distribution of the digital mask is established, the expression is as follows:
Figure FDA0003085877610000021
wherein M is a discrete matrix form of complex amplitude transmittance M (x, y) of the digital mask, and M is am，n(x-mdx，y-ndy) The core is u (x-md)x，y-ndy) A discrete representation of (a) representing a sampling matrix for a single pixel of the digital mask;
Figure FDA0003085877610000022
representing the kronecker product.
6. The method of claim 5, wherein the optical model of the digital mask projection lithography imaging model is built with a discrete matrix of the complex amplitude transmittance of the digital mask, and the expression formula is as follows:
Figure FDA0003085877610000023
the resulting lithographic pattern Z is then expressed as:
Figure FDA0003085877610000024
in the formula, T { M } represents a lithography forward system, and represents a lithography pattern obtained by receiving the digital mask M.
7. The method of claim 6, wherein the digital mask inversion calculation is performed for a given binary target pattern
Figure FDA0003085877610000025
Finding a digital mask
Figure FDA0003085877610000026
And loaded on the spatial light modulator to make the photoetching pattern Z epsilon RN×NAnd the target pattern
Figure FDA0003085877610000027
With the smallest distance, the cost function F is expressed as:
Figure FDA0003085877610000028
in the formula, NMThe number of pixels arranged in a certain direction of the digital mask;
Figure FDA0003085877610000029
representing the square of the F-norm.
8. The method of claim 7, wherein during the calculation of the inversion of the digital mask, when the digital mask is loaded with only gray scale amplitude and not phase-modulated, the pixels in row i and column j of the digital mask MMi，j∈[0，1]Wherein i, j is 1, 2MThen there is an optimization problem:
Figure FDA00030858776100000210
wherein,
Figure FDA0003085877610000031
θi，j∈[-∞，+∞]；
when the digital mask is loaded with gray scale amplitude and the phase thereof is 0 or pi, the pixel M of the ith row and the jth column of the digital mask Mi，j∈[-1，1]Wherein i, j is 1, 2MThen there is an optimization problem:
M＝cosθ
wherein,
Figure FDA0003085877610000032
θi，j∈[-∞，+∞](ii) a Wherein theta denotes a digital mask, thetai，jRepresenting the elements in the ith row and jth column of the digital mask theta.
9. The method according to claim 8, wherein during the optimization of the digital mask projection lithography imaging model, the gradient of the cost function F to the digital mask is calculated using a steepest descent method according to the optimization problem.
10. A digital mask projection lithography optimization system, applied to the digital mask projection lithography optimization method according to any one of claims 1 to 9, comprising an on-axis point light source, a spatial light modulator, and a processor, wherein:
the processor performing the steps of the digital mask projection lithography optimization method of any one of claims 1 to 9;
the on-axis point light source generates an optimized digital mask M through the processor and then is loaded on the on-axis point light sourceOn the spatial light modulator, obtaining a target pattern
Figure FDA0003085877610000033
The smallest difference lithographic pattern Z.
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