CN114740557B - Method for designing linear density of fringe by eliminating aberration and changing grating pitch in raster scanning photoetching - Google Patents

Method for designing linear density of fringe by eliminating aberration and changing grating pitch in raster scanning photoetching Download PDF

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CN114740557B
CN114740557B CN202210041105.6A CN202210041105A CN114740557B CN 114740557 B CN114740557 B CN 114740557B CN 202210041105 A CN202210041105 A CN 202210041105A CN 114740557 B CN114740557 B CN 114740557B
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宋�莹
张刘
刘玉娟
朱杨
章家保
王文华
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Jilin University
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Abstract

The invention provides a fringe line density design method for eliminating aberration and variable-pitch grating scanning photoetching, relates to the technical field of holographic grating manufacture, and provides an interference fringe line density design method for eliminating aberration and variable-pitch grating scanning photoetching. The line density change rule of the photoetching interference fringes can be designed according to the method. The precision of the groove density of the variable-pitch grating is improved, the controllability of the exposure contrast process parameters is ensured, and the method has important significance for improving the scanning photoetching manufacturing level of the variable-pitch grating and improving the success rate of grating manufacturing.

Description

Method for designing linear density of fringe by eliminating aberration and changing grating pitch in raster scanning photoetching
Technical Field
The invention relates to the technical field of holographic grating manufacture, in particular to a design method of interference fringe line density of aberration-eliminating variable-pitch grating scanning photoetching.
Background
The aberration-eliminating variable-pitch grating is a plane grating with grating groove density changing according to a certain rule, and optical aberrations such as defocusing, spherical aberration and the like are corrected through the change of the grating groove density. Compared with the curved surface grating, the grating substrate is a plane, and the processing difficulty of the substrate is reduced. The meridian light incident to the grating with the variable grating pitch can form spectral lines by itself, extra collimating and focusing optical elements are not needed in a spectral instrument, the volume and the weight of the instrument are reduced, the light energy utilization rate is improved, the laser damage threshold is high, and the method has important application in the fields of synchronous radiation light source devices, high-energy laser devices and the like.
The variable pitch grating is usually fabricated by mechanical scribing, electron beam direct writing, laser direct writing, holographic exposure and the like. The manufacturing modes of mechanical scribing, electron beams, laser direct writing and the like belong to ultra-precision machining, the machining of grating grooves is completed line by line, the manufacturing efficiency is low, and the change of adjacent grating pitches of the variable-pitch grating is generally not more than the nanometer level, so that the requirements on corresponding ultra-precision machining equipment and machining conditions are high, and the manufacturing difficulty and the manufacturing cost are high. The conventional holographic exposure method for manufacturing a variable-pitch grating can adopt a spherical wave or aspheric wave exposure system, but the adjustable freedom degree of the spherical wave exposure system is less, and the problem of groove bending exists, which can cause the reduction of the resolution capability of the grating. Aspheric wave exposure system design, processing and debugging difficulty are large, the process is not easy to realize, and large error exists between the actual grating groove density and the expected value.
The variable period scanning photoetching is another important method for manufacturing the variable grating pitch grating, an interference optical system forms an interference pattern with a small caliber (micrometer-millimeter magnitude), a two-dimensional worktable bears a grating substrate to carry out step scanning movement, relative movement is generated between the interference pattern and the grating substrate, and interference fringes are recorded in photoresist coated on the grating substrate until the exposure of the whole effective area of the grating substrate is completed. In order to realize the manufacturing of the variable-pitch grating, in the exposure process, the interference included angle of coherent light beams is changed through precise photoelectric control according to the change function of the line density of interference fringes for photoetching, and the line density of the interference fringes is continuously and precisely adjusted, so that the groove density of the manufactured grating meets the requirement of a design index. The variable-pitch grating manufactured by the manufacturing method has no problem of groove bending, hundreds of interference fringes exist in the interference pattern, the manufacturing efficiency is greatly improved, and a large-caliber optical system is not needed when large-area grating manufacturing is carried out.
However, if the density variation function of the interference fringe lines is equal to the target groove density function of the variable-pitch grating, the density of the interference fringe lines is adjusted, and the groove density of the manufactured variable-pitch grating has larger deviation from a design value. This is mainly due to the following two reasons that when the line density of the interference fringes is changed by the variable-period scanning lithography system, the line densities of all the interference fringes in the interference pattern are changed identically, and the interference fringes cannot be precisely adjusted from one line pitch to another. And the intensity distribution of the interference patterns is Gaussian distribution, in order to ensure the uniformity of the exposure, a certain overlap exists between the interference patterns of adjacent scanning sections, and the manufactured grating groove distribution has a homogenization effect.
The establishment of a design method of interference fringe line density is a key problem in the application of the variable period scanning lithography technology. The invention provides a method for designing the linear density of interference fringes for aberration-eliminating variable-pitch grating scanning photoetching.
Disclosure of Invention
The invention provides an interference fringe line density design method for aberration-eliminating variable-pitch grating scanning photoetching, which can be used for designing an interference fringe line density function in a scanning photoetching process according to a variable-pitch grating groove density target function, designing the function according to the interference fringe line density, changing the line density of interference fringes, and finally obtaining the variable-period grating groove density which meets the requirements of the grating groove density target function.
The method for designing the linear density of the fringe of the optical grating scanning photoetching with the aberration elimination and the variable pitch comprises the following steps:
step one, determining a groove density function of a variable-pitch grating and general photoetching process manufacturing parameters;
step one, according to the aberration elimination characteristic of the variable-pitch grating and the application requirement of the variable-pitch grating in an instrument, designing a target function g (x) of the groove density of the variable-pitch grating as follows:
g(x)＝n g0 +n g1 (x-W g /2)+n g2 (x-W g /2) 2 +n g3 (x-W g /2) 3
ideal phase distribution phi of the grating g (x) Expressed as:
Φ g (x)＝2πg(x)·x
wherein x is the coordinate of the vector direction of the grating, x =0 is located at the grating boundary, W g Is the total width in the direction of the grating vector, n g0 Is the groove density at the center of the grating, n g1 Coefficient of first order of grating groove density, n g2 Coefficient of quadratic term, n, for grating groove density g3 The coefficient of the cubic term of the grating groove density; n is g0 、 n g1 、n g2 And n g3 Determining according to the variable-pitch grating aberration correction principle and the use parameters of a spectroscopic instrument or a laser device;
determining the following manufacturing parameters when the variable-period grating is manufactured according to the design and the debugging parameters of the variable-period scanning photoetching system and the target function of the groove density of the variable-pitch grating obtained in the step one by one:
setting the radius of Gaussian beam waist of interference pattern to be R ho The overlapping width of the interference patterns of the adjacent scanning sections accounts for the radius R of the beam waist ho The ratio StepRatio, the width of the interference pattern overlap is StepRatio R ho ；
Setting the total step number of step scanning as N, wherein N is more than or equal to W g /(R ho StepRatio) +1, making the width of the exposure area greater than the effective width of the grating;
the step number of each step of step scanning is N steps ，N steps ＝round(R ho ·StepRatio·n g0 ) (ii) a round () is a round integer function;
step two, calculating the grating phase distribution error phi when the density change function f (x) of the interference fringe lines is equal to the groove density function g (x) of the grating with the variable grating pitch according to the calculation method of the total exposure of the variable period scanning photoetching e (x)；
The method for calculating the total exposure of the variable-period scanning photoetching comprises the following steps:
setting the interference fringe line density variation function f (x) and the variable-pitch grating groove density target function g (x) to have the same form, and expressing the form as follows:
f(x)＝m 0 +m 1 (x-W g /2)+m 2 (x-W g /2) 2 +m 3 (x-W g /2) 3
in the formula, m 0 Coefficient of constant term being a function of variation of the linear density of the interference fringes, m 1 Coefficient of first order term, m, being a function of variation of line density of interference fringes 2 Coefficient of quadratic term, m, being a function of the variation of the linear density of the interference fringes 3 Coefficient of cubic term of density variation function of interference fringe line; starting a scanning photoetching initial scanning segment from x =0, wherein the corresponding step number k =0 when x =0, the initial scanning is the 1 st scanning, and the corresponding exposure is D 0 (x)，S k Step distance of the k step;
S 0 ＝0，
Figure BDA0003470252210000041
is the total distance from step 0 to step k,
Figure BDA0003470252210000042
after k steps are carried out, the line density of interference fringes of the (k + 1) th scanning is obtained; delta k ＝f k -f k-1 Is the difference between the interference fringe line density of k +1 scans and k scans, and when k =0, Δ 0 =0, when k>At the time of 0, the number of the first,
Figure BDA0003470252210000043
exposure D for the k +1 th scan after the k step k (x) And phase difference between the (k + 1) th scan and the initial scan
Figure BDA0003470252210000044
Comprises the following steps:
Figure BDA0003470252210000045
Figure BDA0003470252210000046
wherein B (x) is the background component of the single-scan exposure, and A (x) is the Gaussian-distributed exposure intensity envelope in the single-scan exposure;
Figure BDA0003470252210000047
when photoetching is finished, the total exposure on the grating is the superposition D of the exposure of N +1 times of scanning after the total steps of step scanning are N steps tot (x) Namely:
D tot (x)＝D 0 (x)+D 1 (x)+…D N (x)
＝B tot (x)+A tot (x)sin(Ψ tot (x))
in the formula, B tot (x) Background component of total exposure, A tot (x) The amplitude of the AC component of the total exposure;
Figure BDA0003470252210000048
Figure BDA0003470252210000049
Figure BDA0003470252210000051
Figure BDA0003470252210000052
Ψ tot (x)＝2πxf 0 +Ψ(x)
Ψ(x)＝arctan[F(x)/E(x)]
in the formula, Ψ tot (x) Psi (x) is the phase increment between the total exposure and the 1 st scan, psi tot (x) Equal to the actual phase distribution of the manufactured variable pitch grating; γ (x) = A tot (x)/B tot (x) Is the total exposure contrast;
setting f (x) = g (x), i.e., m 0 ＝n g0 ，m 1 ＝n g1 ，m 2 ＝n g2 ，m 3 ＝n g3 Calculating the phase variation Ψ of the exposure by using the method for calculating the total exposure of variable period scanning lithography tot (x) The error of the grating phase distribution between the actual phase distribution of the manufactured variable pitch grating and the ideal phase distribution of the grating is phi e (x)＝ Ψ tot (x)-Φ g (x)；
Step three, designing a three-order term coefficient m of an interference fringe line density change function through a data fitting and iterative optimization method 3 Optimized design value of (m) 3_optimal ；
Step four, designing a secondary term coefficient m of the interference fringe linear density variation function through a data fitting and iterative optimization method 2 Optimized design value of (m) 2_optimal ；
Step five, designing an optimized design value m of a first-order coefficient m1 of the interference fringe line density change function through a data fitting and iterative optimization method 1_optimal ；
Step six, designing a constant term coefficient m of a linear density change function of the interference fringe 0 Optimized design value of (m) 0_optimal ；
Step seven, optimizing m according to the step three to the step six 3_optimal 、m 2_optimal 、m 1_optimal And m 0_optimal Checking whether the exposure contrast meets the requirements of the exposure process;
the optimized and designed interference fringe line density change function is as follows:
f optimal (x)＝m 0_optimal +m 1_optimal (x-W g /2)+m 2_optimal (x-W g /2) 2 +m 3_optimal (x-W g /2) 3 ；
calculating to obtain an exposure contrast gamma (x) according to the method for calculating the total exposure of the variable-period scanning photoetching given in the second step, judging whether the exposure contrast gamma (x) meets the requirement of the exposure contrast within the whole range of x, if not, reducing the ratio StepRatio of the overlapping width of the interference patterns in the second step to the beam waist radius, and executing the second step to the seventh step again until the gamma (x) meets the requirement of the exposure contrast;
if so, finishing the whole optimization process and designing the interference fringe line density change function f according to the optimization optimal (x) And changing the linear density of interference fringes in the photoetching process to obtain the variable-pitch grating with the target groove density.
The invention has the following positive effects: the invention relates to an interference fringe line density design method for aberration-eliminating variable-pitch grating scanning photoetching, which is used for manufacturing a variable-pitch grating by a variable-period scanning interference photoetching system. According to the known groove density of the variable-pitch grating, the line density variation rule of the photoetching interference fringes can be designed according to the method. The precision of the groove density of the variable-pitch grating is improved, the controllability of the exposure contrast process parameters is ensured, and the method has important significance for improving the scanning photoetching manufacturing level of the variable-pitch grating and improving the success rate of grating manufacturing.
Drawings
FIG. 1 is a simplified schematic diagram of a variable period scanning lithography apparatus used in the method for designing the linear density of interference fringes for aberration-reducing variable pitch grating scanning lithography according to the present invention.
FIG. 2 is a schematic diagram of coordinate system definition.
FIG. 3 is a schematic diagram of interference pattern beam waist radius and overlay lithography.
FIG. 4 is a phase distribution Φ of a variable pitch grating g (x) And changing the linear density of the interference fringes according to the grating groove density function to obtain the grating phase distribution psi tot (x)(n g0 ＝1200gr/mm，n g1 ＝-0.7783gr/mm 2 ， n g2 ＝1.865×10 -4 gr/mm 3 ，n g3 ＝-8.1336×10 -8 gr/mm 4 ，W g =30 mm).
FIG. 5 shows the grating phase distribution error phi obtained by varying the density of interference fringe lines according to the grating groove density function e (x)＝Ψ tot (x)-Φ g (x) The grating parameter effect diagram is the same as that in FIG. 4.
FIG. 6 is a drawing showingCubic coefficient m of interference fringe line density 3_optimal The optimization design flow chart of (1).
FIG. 7 is a phase distribution Φ of a variable pitch grating g (x) And changing the density of interference fringe lines according to the density of interference fringe lines obtained by the design method to obtain a grating phase distribution psi tot (x)(n g0 ＝1200gr/mm， n g1 ＝-0.7783gr/mm 2 ，n g2 ＝1.865×10 -4 gr/mm 3 ，n g3 ＝-8.1336×10 -8 gr/mm 4 ，W g ＝30mm，Rho＝0.1mm，ξ 1order ＝ξ 2order ＝ξ 3order ＝ξ 4order =1e-4 rad).
FIG. 8 shows the phase distribution error Φ of the grating obtained according to the design value e (x)＝Ψ tot (x)-Φ g (x) Effect graphs;
fig. 9 is a graph showing the effect of the exposure contrast γ (x) obtained according to the design value.
Detailed Description
The present embodiment is described with reference to fig. 1 to fig. 9, which illustrate a method for designing the line density of interference fringes for aberration-reducing variable-pitch grating scanning lithography, and the method is mainly applied to a variable-period scanning lithography system, and is composed as shown in fig. 1, in which several measurement and control elements are removed. In the figure, 1 and 2 are two coherent light beams, 3 and 4 are interference light beam adjusting mirrors, 5 is a semi-reflecting and semi-transparent mirror, 6 and 7 are lenses, and the interference light beam adjusting mirrors are used for forming a 4f optical system, so that interference of 1 and 2 is realized to form an interference pattern 8, and the intensity of the interference pattern 8 is in Gaussian distribution. 3 and 4 are located at the front focal plane position of 6, and 11 is an interference fringe linear density control system, and the linear density of interference fringes in the interference pattern can be adjusted by adjusting the interference angles of the coherent light beams 1 and 2 through 3 and 4 according to an interference fringe linear density function. The grating substrate 9 is coated with photoresist, and the two-dimensional motion worktable 10 is used for bearing the grating substrate 9 to carry out step-and-scan motion.
The method proposed by the present embodiment comprises the following steps:
step one, determining a groove density function of the variable-pitch grating and manufacturing parameters of a general photoetching process.
According to the aberration eliminating characteristic of the variable-pitch grating and the application requirement of the variable-pitch grating in an instrument, designing a groove density objective function of the variable-pitch grating as follows:
g(x)＝n g0 +n g1 (x-W g /2)+n g2 (x-W g /2) 2 +n g3 (x-W g /2) 3
the coordinate system of the grating is defined as shown in FIG. 2, and the ideal phase distribution Φ of the grating g (x) Can be expressed as
Φ g (x)＝2πg(x)·x
Wherein g (x) is the target groove density of the grating with variable grating pitch, x is the coordinate of the vector direction of the grating, x =0 is positioned at the boundary of the grating, and W g Is the total width of the vector direction of the grating, n g0 The groove density at the center of the grating is expressed in gr/mm (the number of grooves contained in each mm), n g1 Is the first order coefficient of the grating groove density, and the unit is gr/mm 2 ，n g2 Is the quadratic coefficient of the grating groove density, and the unit is gr/mm 3 ，n g3 Coefficient of cubic term of grating groove density in unit of gr/mm 4 。n g0 、n g1 、n g2 、n g3 And determining according to the variable-pitch grating aberration correction principle and the use parameters of a spectroscopic instrument or a laser device.
According to the basic composition and operation of a variable period scanning lithography system, as shown in FIG. 1, to ensure uniformity of the amount of exposure, there is an overlap between the interference patterns of adjacent scan segments. According to the design, the installation and adjustment parameters of the system and the groove density function of the variable-pitch grating, the following manufacturing parameters are determined when the variable-period grating is manufactured:
the radius of the Gaussian beam waist of the interference pattern is R ho 。
The ratio StepRatio of the overlapping width of the interference patterns of the adjacent scanning segments to the radius of the beam waist, the overlapping width of the interference patterns is StepRatio × R ho In order to ensure the uniformity of the exposure, stepRatio is required to be less than 0.9, and the smaller StepRatio is, the higher the uniformity of the exposure is, but the larger the total number of scanning steps is, the lower the manufacturing efficiency is. As shown in fig. 3.
Step scanningThe total number of steps N, N is not less than W g /(R ho Steplatio) +1, making the width of the exposure area larger than the effective width of the grating.
Step number N of each step of step-by-step scanning steps ，N steps ＝round(R ho ·StepRatio·n g0 )。
And step two, establishing a variable period scanning photoetching total exposure calculation method, and calculating the exposure phase change psi (x) and the exposure contrast gamma when the grating groove density function is used as an interference fringe line density change function f (x).
The method for calculating the total exposure of the variable-period scanning photoetching comprises the following steps:
the interference fringe line density variation function and the grating groove density function have the same form and can be expressed as:
f(x)＝m 0 +m 1 (x-W g /2)+m 2 (x-W g /2) 2 +m 3 (x-W g /2) 3
in the formula, m 0 Coefficient of constant term being a function of variation of the linear density of the interference fringes, m 1 Coefficient of first order term, m, being a function of variation of line density of interference fringes 2 Coefficient of quadratic term, m, being a function of the variation of the linear density of the interference fringes 3 Coefficient of cubic term of density variation function of interference fringe line; the scanning photoetching initial scanning segment starts from x =0, and the number of the scanning steps is k =0,S k Step distance of the k-th step, S 0 ＝0，
Figure BDA0003470252210000081
The total distance from x =0 to the kth step,
Figure BDA0003470252210000082
interference fringe line density for the k +1 th scan after stepping for k steps. Delta k ＝f k -f k-1 Is the difference between the interference fringe line density of k +1 scans and k scans, and when k =0, Δ 0 =0, when k>At the time of 0, the number of the first,
Figure BDA0003470252210000083
exposure D for the k +1 th scan after the k step k (x) And phase difference between the (k + 1) th scan and the initial scan
Figure BDA0003470252210000091
Comprises the following steps:
Figure BDA0003470252210000092
Figure BDA0003470252210000093
where B (x) is the background intensity of the exposure and A (x) is the intensity envelope of the Gaussian-distributed interference pattern.
Figure BDA0003470252210000094
When photoetching is finished, the total exposure on the grating is the superposition D of the exposure of N +1 times of scanning after the total steps of step scanning are N steps tot (x) Namely:
D tot (x)＝D 0 (x)+D 1 (x)+…D N (x)
＝B tot (x)+A tot (x)sin(2πxf 0 +Ψ)
B tot (x) Background component of total exposure, A tot (x) The amplitude of the alternating current component of the total exposure;
Figure BDA0003470252210000095
Figure BDA0003470252210000096
Figure BDA0003470252210000097
Figure BDA0003470252210000098
Ψ tot (x)＝2πxf 0 +Ψ(x)
Ψ(x)＝arctan[F(x)/E(x)]
in this embodiment, in addition to using the general photolithography process parameters in the first step, the following design parameters are set:
(1) Setting the density function of interference fringe lines to be equal to the groove density function of the grating with variable grating pitch, i.e. m 0 ＝n g0 ，m 1 ＝n g1 ，m 2 ＝n g2 ，m 3 ＝n g3 。
(2) The change in B (x) does not affect the design of the interference fringe line density, and B (x) = a (x) is set, and the contrast of a single scanning exposure is 1.
(3) Step distance S of the kth step k One of the following three stepping modes can be selected, different interference fringe design values can be obtained according to the method of the embodiment, and the precision requirement of the groove density of the variable-pitch grating can be met:
①S k ＝N steps /f k-1 。
②S k ＝2N steps /(f k +f k-1 )，
Figure BDA0003470252210000101
③S k ＝N steps /f k ，
Figure BDA0003470252210000102
according to the parameters of the step one and the parameters, by adopting a numerical calculation method and a method for calculating the total exposure of variable-period scanning photoetching, a psi (x) changing curve along with x, psi (x) and phi can be obtained g (x) As shown in fig. 4. The phase error between the two is phi e (x)＝Ψ(x)-Φ g (x) As shown in FIG. 5, the density of the interference fringe lines is adjusted according to the groove density function of the grating with variable grating pitch e (x) Not equal to 0, the variable pitch grating obtained by photoetching has a large difference from the groove density of a designed value.
Step three, designing a three-order term coefficient m of an interference fringe line density change function through a data fitting and iterative optimization method 3 Optimized design value of (m) 3_optimal 。
Adopting a polynomial curve fitting algorithm to correct the phase distribution error phi obtained in the step two e (x) Performing a fourth polynomial curve fit of phi e (x) Has a fitting polynomial of phi ep (x)＝2π(a 40 x 4 +a 30 x 3 +a 20 x 2 +a 10 x+a 00 )，a 40 、 a 30 、a 20 、a 10 And a 00 Respectively fitting a polynomial of four times phi ep (x) The coefficient of (a);
quartic phase error threshold value xi of optimal design for setting coefficient m3 of interference fringe linear density change function f (x) 4order M is obtained by calculation through a one-dimensional search iterative optimization method 3_optimal The iterative process is as follows, and the flow chart is shown in fig. 6.
(1) Setting search range [ a ] of iterative optimization m3 (0) ,b m3 (0) ]，a m3 (0) ＝m 3_nearby -H m3 ，b m3 (0) ＝ m 3_nearby +H m3 ，2H m3 Is m 3 Breadth of initial search range of optimum value, number of iterations i m3 ＝0，m 3_nearby Is the optimal solution m 3_optimal Initial approximation of, m 3_nearby ＝n g3 2 /(n g3 +a 40 ) The maximum phase error of the initial quartic term is phi e_4order_m3 (0) ＝abs(2πa 40 W g 4 )；
(2) If it is
Figure BDA0003470252210000111
Not satisfying the thresholdPerforming steps (3) to (7) when the value is required, otherwise, exiting the loop and performing step (8);
(3) By using a one-dimensional search method (e.g. golden section, fibonacci, etc.) in
Figure BDA00034702522100001126
Internally determined optimization variables
Figure BDA00034702522100001127
And
Figure BDA00034702522100001128
Figure BDA00034702522100001129
(4) According to the optimization variables
Figure BDA00034702522100001130
Value setting of linear density variation function of interference fringe
Figure BDA0003470252210000112
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure BDA0003470252210000113
Figure BDA0003470252210000114
Corresponding phase error
Figure BDA0003470252210000115
To pair
Figure BDA0003470252210000116
A fourth-order polynomial fitting is performed,
Figure BDA0003470252210000117
is a fitting polynomial of
Figure BDA0003470252210000118
Record coefficient of quartic item
Figure BDA0003470252210000119
(5) According to the optimization variables
Figure BDA00034702522100001110
Value setting of linear density variation function of interference fringe
Figure BDA00034702522100001111
Calculating according to the variable period scanning photoetching total exposure quantity calculation method given in the step two
Figure BDA00034702522100001112
Figure BDA00034702522100001113
Corresponding phase error
Figure BDA00034702522100001114
To pair
Figure BDA00034702522100001115
A fourth-order polynomial fitting is performed,
Figure BDA00034702522100001116
is a fitting polynomial of
Figure BDA00034702522100001117
Recording the coefficient of four items
Figure BDA00034702522100001118
(6) If it is
Figure BDA00034702522100001119
Then the
Figure BDA00034702522100001120
Figure BDA00034702522100001121
If not, then,
Figure BDA00034702522100001122
then the
Figure BDA00034702522100001123
Figure BDA00034702522100001124
(7)i m3 ＝i m3 +1, return to step (2);
(8)
Figure BDA00034702522100001125
step four, designing a secondary term coefficient m of the interference fringe linear density variation function through a data fitting and iterative optimization method 2 Optimized design value of (m) 2_optimal The iterative process is as follows:
(1) M obtained according to step three 3_optimal Setting the linear density variation function f of the interference fringe 3optimal ＝n g0 +n g1 ·(x-W g /2)+n g2 ·(x-W g /2) 2 +m 3_optimal ·(x-W g /2) 3 Calculating to obtain psi according to the calculation method of the total exposure of the variable-period scanning photoetching given in the step two tot_3optimal Error of phase phi e_3optimal ＝Ψ tot_3optimal -Φ g To phi e_3optimal Performing a fourth order polynomial fit of phi e_3optimal Has a fitting polynomial of phi ep_3optimal (x)＝2π(a 4_ 3optimal x 4 +a 3_3optimal x 3 +a 2_3optimal x 2 +a 1_3optimal x+a 0_3optimal ) Recording the cubic term coefficient a 3_3optimal ；
Cubic term phase error threshold xi of optimized design for setting coefficient m2 of interference fringe linear density change function f (x) 3order ；
(2) Search for setting iterative optimizationRange [ a ] m2 (0) ,b m2 (0) ]，a m2 (0) ＝m 2_nearby -H m2 ，b m2 (0) ＝ m 2_nearby +H m2 ，2H m2 Is m 2 Breadth of initial search range of optimum value, number of iterations i m2 ＝0，m 2_nearby Is the optimal solution m 2_optimal To an initial approximation of the first,
Figure BDA0003470252210000121
initial cubic phase error maximum of phi e_3order_m2 (0) ＝abs(2πa 3_3optimal W g 3 )；
(3) If it is
Figure BDA0003470252210000122
If the threshold requirement is not met, executing the steps (4) to (8), otherwise, exiting the loop and executing the step (9);
(4) By using a one-dimensional search method (e.g. golden section, fibonacci, etc.) in
Figure BDA0003470252210000123
Internally determined optimization variables
Figure BDA0003470252210000124
And
Figure BDA0003470252210000125
Figure BDA0003470252210000126
(5) According to the optimization variables
Figure BDA0003470252210000127
Value setting of linear density variation function of interference fringe
Figure BDA0003470252210000128
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step twoTo obtain
Figure BDA0003470252210000129
Figure BDA00034702522100001210
Corresponding phase error
Figure BDA00034702522100001211
To pair
Figure BDA00034702522100001212
A fourth-order polynomial fitting is performed,
Figure BDA00034702522100001213
is a fitting polynomial of
Figure BDA00034702522100001214
Recording cubic item coefficients
Figure BDA00034702522100001215
(6) According to the optimization variables
Figure BDA00034702522100001216
Value setting of the linear density variation function of the interference fringes
Figure BDA00034702522100001217
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure BDA0003470252210000131
Figure BDA0003470252210000132
Corresponding phase error
Figure BDA0003470252210000133
For is to
Figure BDA0003470252210000134
To carry outA fourth-order polynomial fitting is carried out,
Figure BDA0003470252210000135
is a fitting polynomial of
Figure BDA0003470252210000136
Recording cubic item coefficients
Figure BDA0003470252210000137
(7) If it is
Figure BDA0003470252210000138
Then the
Figure BDA0003470252210000139
Figure BDA00034702522100001310
If not, then,
Figure BDA00034702522100001311
then
Figure BDA00034702522100001312
Figure BDA00034702522100001313
(8)i m2 ＝i m2 +1, return to step (3);
(9)
Figure BDA00034702522100001314
step five, designing an optimized design value m of a first-order coefficient m1 of the interference fringe line density change function through a data fitting and iterative optimization method 1_optimal The iterative process is as follows:
(1) M obtained according to step four 2_optimal Setting the linear density variation function f of the interference fringe 2optimal ＝n g0 +n g1 ·(x-W g /2)+m 2_optimal ·(x-W g /2) 2 +m 3_optimal ·(x-W g /2) 3 Calculating to obtain psi according to the calculation method of the total exposure of the variable-period scanning photoetching given in the step two tot_2optimal Error of phase phi e_2optimal ＝Ψ tot_2optimal -Φ g To phi e_2optimal Performing a fourth order polynomial fit of phi e_2optimal Is a fitting polynomial of phi ep_2optimal (x)＝2π(a 4_ 2optimal x 4 +a 3_2optimal x 3 +a 2_2optimal x 2 +a 1_2optimal x+a 0_2optimal ) Recording the coefficient of quadratic term a 2_2optimal ；
Quadratic term phase error threshold xi of optimized design for setting coefficient m1 of interference fringe linear density change function f (x) 2order ；
(2) Setting search range [ a ] of iterative optimization m1 (0) ,b m1 (0) ]，a m1 (0) ＝m 1_nearby -H m1 ，b m1 (0) ＝ m 1_nearby +H m1 ，2H m1 Is m 1 Breadth of initial search range of optimum value, number of iterations i m1 ＝0，m 1_nearby Is the optimal solution m 1_optimal To an initial approximation of the value of (a),
Figure BDA00034702522100001315
initial quadratic phase error maximum of phi e_2order_m1 (0) ＝abs(2πa 2_2optimal W g 2 )；
(3) If it is
Figure BDA0003470252210000141
If the threshold requirement is not met, executing the steps (4) to (8), otherwise, exiting the loop and executing the step (9);
(4) Using a one-dimensional search method (e.g., golden section, fibonacci, etc.) at [ a m1 (im1) ,b m1 (im1) ]Internally determined optimization variable m 1L (im1) And m 1R (im1) ，a m1 (im1) ≤m 1L (im1) <m 1R (im1) ≤ b m1 (im1) ；
(5) According to the optimization variable m 1L (im1) Value setting of linear density variation function of interference fringe
Figure BDA0003470252210000142
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure BDA0003470252210000143
m 1L (im1) Corresponding phase error
Figure BDA0003470252210000144
To pair
Figure BDA0003470252210000145
A fourth-order polynomial fitting is performed,
Figure BDA0003470252210000146
is a fitting polynomial of
Figure BDA0003470252210000147
Recording secondary item coefficients
Figure BDA0003470252210000148
(6) According to the optimization variable m 1R (im1) Value setting of linear density variation function of interference fringe
Figure BDA0003470252210000149
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure BDA00034702522100001410
m 1R (im1) Corresponding phase error
Figure BDA00034702522100001411
To pair
Figure BDA00034702522100001412
A fourth-order polynomial fitting is performed,
Figure BDA00034702522100001413
is a fitting polynomial of
Figure BDA00034702522100001414
Record secondary item coefficients
Figure BDA00034702522100001415
(7) If it is
Figure BDA00034702522100001416
Then a m1 (im1+1) ＝m 1L (im1) ，b m1 (im1+1) ＝b m1 (im1) ，
Figure BDA00034702522100001417
If not, then,
Figure BDA00034702522100001418
then a m1 (im1+1) ＝a m1 (im1) ， b m1 (im1+1) ＝m 1R (im1) ，
Figure BDA00034702522100001419
(8)i m1 ＝i m1 +1, returning to the step five;
(9)m 1_optimal ＝(m 1L (im1) +m 1R (im1) )/2。
step six, designing a constant term coefficient m of a linear density change function of the interference fringe 0 Optimized design value of (m) 0_optimal The iterative process is as follows:
(1) M obtained according to step five 1_optimal Setting the linear density variation function f of the interference fringe 1optimal ＝n g0 +m 1_optimal ·(x-W g /2)+m 2_optimal ·(x-W g /2) 2 +m 3_optimal ·(x-W g /2) 3 Calculating to obtain psi according to the calculation method of the total exposure of the variable-period scanning photoetching given in the step two tot_1optimal Error of phase phi e_1optimal ＝Ψ tot_1optimal -Φ g To phi e_1optimal Performing a fourth order polynomial fit of phi e_1optimal Has a fitting polynomial of phi ep_1optimal (x)＝2π(a 4_1optimal x 4 +a 3_1optimal x 3 +a 2_1optimal x 2 +a 1_1optimal x+a 0_1optimal ) Recording the coefficient of a primary term 1_1optimal ；
Setting primary term phase error threshold value xi of coefficient m0 optimization design of interference fringe line density change function f (x) 1order ；
(2) Setting search range [ a ] of iterative optimization m0 (0) ,b m0 (0) ]，a m0 (0) ＝m 0_nearby -H m0 ，b m0 (0) ＝ m 0_nearby +H m0 ，2H m0 Is m 0 Breadth of initial search range of optimum value, number of iterations i m0 ＝0，m 0_nearby Is the optimal solution m 0_optimal Initial approximation of, m 0_nearby ＝n g0 -a 1_1optimal The maximum value of the initial primary phase error is phi e_1order_m0 (0) ＝abs(2πa 1_1optimal W g )；
(3) If it is
Figure BDA0003470252210000151
If the threshold requirement is not met, executing the steps (4) to (8), otherwise, exiting the loop and executing the step (9);
(4) By using a one-dimensional search method (e.g. golden section, fibonacci, etc.) in
Figure BDA0003470252210000152
Internally determined optimization variables
Figure BDA0003470252210000153
And
Figure BDA0003470252210000154
Figure BDA0003470252210000155
(5) According to the optimization variables
Figure BDA0003470252210000156
Value setting of linear density variation function of interference fringe
Figure BDA0003470252210000157
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure BDA0003470252210000158
Figure BDA0003470252210000159
Corresponding phase error
Figure BDA00034702522100001510
To pair
Figure BDA00034702522100001511
A fourth-order polynomial fitting is performed,
Figure BDA00034702522100001512
is a fitting polynomial of
Figure BDA00034702522100001513
Recording one-time item coefficient
Figure BDA00034702522100001514
(6) According to the optimization variables
Figure BDA00034702522100001515
Value setting of linear density variation function of interference fringe
Figure BDA0003470252210000161
Calculating according to the variable period scanning photoetching total exposure given in the step two
Figure BDA0003470252210000162
Figure BDA0003470252210000163
Corresponding phase error
Figure BDA0003470252210000164
To pair
Figure BDA0003470252210000165
A fourth-order polynomial fitting is performed,
Figure BDA0003470252210000166
is a fitting polynomial of
Figure BDA0003470252210000167
Record one-time item coefficient
Figure BDA0003470252210000168
(7) If it is
Figure BDA0003470252210000169
Then
Figure BDA00034702522100001610
Figure BDA00034702522100001611
If not, then,
Figure BDA00034702522100001612
then the
Figure BDA00034702522100001613
Figure BDA00034702522100001614
(8)i m0 ＝i m0 +1, return to step (3);
(9)
Figure BDA00034702522100001615
step seven, m optimized according to the third step to the seventh step 3_optimal 、m 2_optimal 、m 1_optimal And m 0_optimal And checking whether the exposure contrast meets the requirements of the exposure process.
Setting the interference fringe line density to f optimal (x)＝m 0_optimal +m 1_optimal (x-W g /2)+m 2_optimal (x-W g /2) 2 +m 3_optimal (x-W g /2) 3 And calculating according to the variable-period scanning photoetching total exposure quantity calculation method given in the step two to obtain an exposure contrast ratio gamma (x), and judging whether the exposure contrast ratio gamma meets the exposure contrast ratio requirement in the whole range of x, wherein the exposure contrast ratio requirement is determined by manufacturing process parameters, and if the exposure contrast ratio is required to be more than 0.95.
If gamma does not meet the requirement of exposure contrast, the ratio StepRatio of the overlapping width of the interference pattern in the step one to the radius of the beam waist needs to be reduced, and the steps two, three, four, five, six and seven are carried out again until gamma meets the requirement of exposure contrast.
If gamma meets the exposure contrast requirement, the whole optimization process is ended according to f optimal The linear density of the interference fringes in the photoetching process is changed to obtain the variable-pitch grating with the target groove density, and the optimization result according to the method is shown in fig. 7-9.
In the second embodiment, the present embodiment is an example of the interference fringe line density design method for aberration-reducing variable-pitch grating scan lithography described in the first embodiment:
in this embodiment, the first step, the second step, the third step, the fourth step, the fifth step, the sixth step and the seventh step are set as in the first embodimentThe method is implemented. Wherein the lithographically coherent light beams 1 and 2 are emitted for laser splitting that satisfies the coherence length and exposure wavelength requirements, here from Kr + Laser light was generated at a wavelength of 413.1nm. The opto- mechanical elements 3, 4, 5, 6, 7 are mounted vertically on a stationary optical platform and remain stationary, resulting in a small-sized circular interference pattern.
In step one, the interference pattern Gaussian beam waist radius R ho =100 μm, stepRatio =0.8, and the design parameters of a variable pitch grating are as follows: n is g0 ＝1200gr/mm，n g1 ＝-0.7783gr/mm 2 ，n g2 ＝1.865×10 -4 gr/mm 3 ， n g3 ＝-8.1336×10 -8 gr/mm 4 ，W g =30mm, total scanning steps 400, number of steps N per step steps ＝96。
Step two, step three and step four, can adopt Matlab or Visual studio platform to finish the design process of numerical value calculation. Step two, setting m 0 ＝n g0 ＝1200gr/mm，m 1 ＝n g1 ＝-0.7783gr/mm 2 ， m 2 ＝n g2 ＝1.865×10 -4 gr/mm 3 ，m 3 ＝n g3 ＝-8.1336×10 -8 gr/mm 4 Step by S k ＝N steps /f k-1 。
In step three, xi is set 4order =1e-4rad, and m is obtained by iterative optimization design of golden section method 3_optimal ＝-3.2461×10 -7 gr/mm 4 。
In the fourth step, xi is set 3order =1e-4rad, and m is obtained by iterative optimization design of golden section method 2_optimal ＝5.5583×10 -4 gr/mm 3 。
In step five, xi is set 2order =1e-4rad, and m is obtained by iterative optimization design of golden section method 1_optimal ＝-1.5510gr/mm 2 。
In the sixth step, xi is set 1order =1e-4rad, and m is obtained by iterative optimization design of golden section method 0_optimal ＝1188.2629gr/mm, the rule of the change of the interference fringe line density is f optimal (x)＝m 0_optimal +m 1_optimal (x-W g /2)+m 2_optimal (x-W g /2) 2 +m 3_optimal (x-W g /2) 3 。
And seventhly, calculating to obtain the exposure contrast gamma (x) which is better than 0.99 within the whole grating range of 0-30mm, meeting the process requirement of the exposure contrast gamma (x) of 0.95, and completing the design of the line density of the interference fringes.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is specific and detailed, but not to be understood as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (7)

1. The design method of the linear density of the aberration-eliminating variable-pitch grating scanning photoetching stripes is characterized by comprising the following steps of: the method is realized by the following steps:
firstly, determining a scribed line density function of a variable-pitch grating and general photoetching process manufacturing parameters;
step one, according to the aberration elimination characteristic of the variable-pitch grating and the application requirement of the variable-pitch grating in an instrument, designing a target function g (x) of the groove density of the variable-pitch grating as follows:
g(x)＝n g0 +n g1 (x-W g /2)+n g2 (x-W g /2) 2 +n g3 (x-W g /2) 3
ideal phase distribution phi of the grating g (x) Expressed as:
Φ g (x)＝2πg(x)·x
wherein x is the coordinate of the vector direction of the grating, x =0 is located at the grating boundary, W g Is the total width of the vector direction of the grating, n g0 Is the groove density at the center of the grating, n g1 Coefficient of first order of grating groove density, n g2 Coefficient of quadratic term, n, for grating groove density g3 The coefficient of the cubic term of the grating groove density; n is said g0 、n g1 、n g2 And n g3 Determining according to the variable-pitch grating aberration correction principle and the use parameters of a spectroscopic instrument or a laser device;
step two, according to the design and the adjustment parameters of the variable-period scanning photoetching system and the target function of the groove density of the variable-pitch grating obtained in the step one by one, determining the following manufacturing parameters when the variable-pitch grating is manufactured:
setting the radius of Gaussian beam waist of interference pattern to be R ho The overlapping width of the interference patterns of the adjacent scanning sections accounts for the radius R of the beam waist ho The ratio StepRatio, the width of the interference pattern overlap is StepRatio R ho ；
Setting the total step number of step scanning as N, wherein N is more than or equal to W g /(R ho StepRatio) +1, making the width of the exposure area larger than the effective width of the grating;
the step number of each step of step scanning is N steps ，N steps ＝round(R ho ·StepRatio·n g0 ) (ii) a round () is a round integer function;
step two, calculating the grating phase distribution error phi when the density change function f (x) of the interference fringe lines is equal to the groove density function g (x) of the variable-pitch grating according to the calculation method of the total exposure of the variable-period scanning photoetching e (x)；
The method for calculating the total exposure of the variable-period scanning photoetching comprises the following steps:
setting the interference fringe line density variation function f (x) and the variable-pitch grating groove density target function g (x) to have the same form, and expressing the form as follows:
f(x)＝m 0 +m 1 (x-W g /2)+m 2 (x-W g /2) 2 +m 3 (x-W g /2) 3
in the formula, m 0 Coefficient of constant term, m, being a function of the variation of the linear density of the interference fringes 1 Coefficient of first order term, m, being a function of variation of line density of interference fringes 2 Coefficient of quadratic term, m, being a function of the variation of the linear density of the interference fringes 3 Coefficient of cubic term which is the variation function of interference fringe line density; the scanning photoetching initial scanning segment starts from x =0, the corresponding step number k =0 is x =0, the initial scanning is the 1 st scanning, and the corresponding exposure amount is D 0 (x)，S k Step distance of the k step;
S 0 ＝0，
Figure FDA0003470252200000021
is the total distance from step 0 to step k,
Figure FDA0003470252200000022
interference fringe line density, Δ, for the k +1 th scan after k steps k ＝f k -f k-1 Is the difference between the interference fringe line density of k +1 scans and k scans, and when k =0, Δ 0 =0, when k>At the time of 0, the number of the first,
Figure FDA0003470252200000023
exposure D for the k +1 th scan after the k step k (x) And phase difference between the (k + 1) th scan and the initial scan
Figure FDA0003470252200000024
Comprises the following steps:
Figure FDA0003470252200000025
Figure FDA0003470252200000026
wherein B (x) is the background component of the single-scan exposure, and A (x) is the Gaussian-distributed exposure intensity envelope in the single-scan exposure;
Figure FDA0003470252200000027
when the photoetching is finished, the total exposure on the grating is the superposition D of the exposure of N +1 times of scanning after the total steps of step scanning are N steps tot (x) Namely:
D tot (x)＝D 0 (x)+D 1 (x)+…D N (x)
＝B tot (x)+A tot (x)sin(Ψ tot (x))
in the formula, B tot (x) Background component of total exposure, A tot (x) The amplitude of the AC component of the total exposure;
Figure FDA0003470252200000031
Figure FDA0003470252200000032
Figure FDA0003470252200000033
Figure FDA0003470252200000034
Ψ tot (x)＝2πxf 0 +Ψ(x)
Ψ(x)＝arctan[F(x)/E(x)]
in the formula, Ψ tot (x) Psi (x) is the phase increment between the total exposure and the 1 st scan, psi tot (x) Is equal toActual phase distribution of the manufactured variable-pitch grating; γ (x) = a tot (x)/B tot (x) Is the total exposure contrast;
setting f (x) = g (x), i.e., m 0 ＝n g0 ，m 1 ＝n g1 ，m 2 ＝n g2 ，m 3 ＝n g3 Calculating the phase variation Ψ of the exposure by using the method for calculating the total exposure of variable period scanning lithography tot (x) The error of the grating phase distribution between the actual phase distribution of the manufactured variable pitch grating and the ideal phase distribution of the grating is phi e (x)＝Ψ tot (x)-Φ g (x)；
Step three, designing a cubic term coefficient m of an interference fringe linear density change function through a data fitting and iterative optimization method 3 Optimized design value of (m) 3_optimal ；
Step four, designing a quadratic term coefficient m of the interference fringe linear density variation function through a data fitting and iterative optimization method 2 Optimized design value of (m) 2_optimal ；
Step five, designing an optimized design value m of a first-order coefficient m1 of the interference fringe linear density variation function through a data fitting and iterative optimization method 1_optimal ；
Step six, designing a constant term coefficient m of a linear density change function of the interference fringe 0 Optimized design value of (m) 0_optimal ；
Step seven, optimizing m according to the step three to the step six 3_optimal 、m 2_optimal 、m 1_optimal And m 0_optimal Checking whether the exposure contrast meets the requirements of the exposure process;
the optimized and designed interference fringe line density change function is as follows: f. of optimal (x)＝m 0_optimal +m 1_optimal (x-W g /2)+m 2_optimal (x-W g /2) 2 +m 3_optimal (x-W g /2) 3 ；
Calculating to obtain an exposure contrast gamma (x) according to the method for calculating the total exposure of the variable-period scanning photoetching given in the second step, judging whether the exposure contrast gamma (x) meets the requirement of the exposure contrast within the whole range of x, if not, reducing the ratio StepRatio of the overlapping width of the interference patterns in the second step to the beam waist radius, and executing the second step to the seventh step again until the gamma (x) meets the requirement of the exposure contrast;
if so, ending the whole optimization process according to the optimally designed interference fringe linear density change function f optimal (x) And changing the linear density of interference fringes in the photoetching process to obtain the variable-pitch grating with the target groove density.
2. The method for designing the linear density of the aberration-eliminating variable-pitch grating scanning photoetching stripes according to claim 1, characterized in that:
the change in B (x) does not affect the design of the interference fringe line density, and B (x) = a (x) is set, and the contrast of single scanning exposure is 1.
3. The variable pitch grating scanning lithography fringe line density design method of claim 1, characterized in that:
step distance S of the kth step k One of the following three stepping modes is selected to obtain different interference fringe design values, and the different interference fringe design values all meet the precision requirement of the groove density of the variable-pitch grating:
1. s k ＝N steps /f k-1 ；
2. S k ＝2N steps /(f k +f k-1 )，
Figure FDA0003470252200000041
3. S k ＝N steps /f k ，
Figure FDA0003470252200000042
4. The method for designing the linear density of the aberration-eliminating variable-pitch grating scanning photoetching stripes according to claim 1, characterized in that: the concrete process of the third step is as follows:
using polynomial curvesFitting algorithm for the phase distribution error phi obtained in step two e (x) Performing a fourth order polynomial curve fitting of phi e (x) Has a fitting polynomial of phi ep (x)＝2π(a 40 x 4 +a 30 x 3 +a 20 x 2 +a 10 x+a 00 )，a 40 、a 30 、a 20 、a 10 And a 00 Respectively fitting a polynomial of four times phi ep (x) The coefficient of (a);
setting the coefficient m of the interference fringe linear density variation function f (x) 3 Quartic phase error threshold xi of optimal design 4order M is obtained by calculation through a one-dimensional search iterative optimization method 3_optimal The iterative process is as follows;
step three, setting a search range [ a ] of iterative optimization m3 (0) ,b m3 (0) ]，a m3 (0) ＝m 3_nearby -H m3 ，b m3 (0) ＝m 3_nearby +H m3 ，2H m3 Is m 3 Breadth of initial search range of optimum value, number of iterations i m3 ＝0，m 3_nearby Is the optimal solution m 3_optimal Initial approximation of, m 3_nearby ＝n g3 2 /(n g3 +a 40 ) The initial quartic phase error has a maximum value of phi e_4order_m3 (0) ＝abs(2πa 40 W g 4 )；
Step three, two, if
Figure FDA0003470252200000051
If the requirement of the threshold value is not met, executing the third step to the pseudo-ginseng, otherwise, exiting the circulation and executing the third step and the eighth step;
step three, adopting a one-dimensional searching method (such as golden section method, fibonacci method, bisection method and the like) to perform
Figure FDA00034702522000000522
Internally determined optimization variables
Figure FDA00034702522000000523
And
Figure FDA00034702522000000524
Figure FDA00034702522000000525
Figure FDA00034702522000000526
step three and four, according to the optimization variables
Figure FDA00034702522000000527
Value setting of linear density variation function of interference fringe
Figure FDA0003470252200000052
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure FDA0003470252200000053
Figure FDA00034702522000000529
Corresponding phase error
Figure FDA0003470252200000054
To pair
Figure FDA0003470252200000055
A fourth-order polynomial fitting is performed,
Figure FDA0003470252200000056
is a fitting polynomial of
Figure FDA0003470252200000057
Recording the coefficient of four items
Figure FDA0003470252200000058
Step three and five, according to the optimization variables
Figure FDA0003470252200000059
Value setting of the linear density variation function of the interference fringes
Figure FDA00034702522000000510
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure FDA00034702522000000511
Figure FDA00034702522000000528
Corresponding phase error
Figure FDA00034702522000000512
To pair
Figure FDA00034702522000000513
A fourth-order polynomial fitting is performed,
Figure FDA00034702522000000514
is a fitting polynomial of
Figure FDA00034702522000000515
Recording the coefficient of four items
Figure FDA00034702522000000516
Step three and six, if
Figure FDA00034702522000000517
Then
Figure FDA00034702522000000518
Figure FDA00034702522000000519
If not, then,
Figure FDA00034702522000000520
Figure FDA00034702522000000521
step of Notoginseng, i m3 ＝i m3 +1, returning to the third step;
the steps of,
Figure FDA00034702522000000614
5. The method for designing the linear density of the aberration-eliminating variable-pitch grating scanning photoetching stripes according to claim 1, characterized in that: the concrete process of the step four is as follows:
step four, obtaining m according to step three 3_optimal Setting the linear density variation function f of the interference fringe 3optimal ＝n g0 +n g1 ·(x-W g /2)+n g2 ·(x-W g /2) 2 +m 3_optimal ·(x-W g /2) 3 Calculating to obtain psi according to the calculation method of the total exposure of the variable-period scanning photoetching given in the step two tot_3optimal Error of phase phi e_3optimal ＝Ψ tot_3optimal -Φ g To phi e_3optimal Performing a fourth order polynomial fit of phi e_3optimal Is a fitting polynomial of phi ep_3optimal (x)＝2π(a 4_3optimal x 4 +a 3_3optimal x 3 +a 2_3optimal x 2 +a 1_3optimal x+a 0_3optimal ) Recording the coefficient of cubic term a 3_3optimal ；
Setting a cubic term phase error threshold xi of a coefficient m2 optimization design of an interference fringe linear density variation function f (x) 3order ；
Step four and two, setting the search range [ a ] of iterative optimization m2 (0) ,b m2 (0) ]，a m2 (0) ＝m 2_nearby -H m2 ，b m2 (0) ＝m 2_nearby +H m2 ，2H m2 Is m 2 Breadth of initial search range of optimum value, number of iterations i m2 ＝0，m 2_nearby Is the optimal solution m 2_optimal To an initial approximation of the value of (a),
Figure FDA0003470252200000061
initial cubic phase error maximum of phi e_3order_m2 (0) ＝abs(2πa 3_3optimal W g 3 )；
Step four, three, if
Figure FDA0003470252200000062
If the threshold requirement is not met, executing the step four to the step four eight, otherwise, exiting the circulation and executing the step four nine;
step four, adopting a one-dimensional searching method in
Figure FDA0003470252200000063
Internally determined optimization variables
Figure FDA0003470252200000064
And
Figure FDA0003470252200000065
Figure FDA0003470252200000066
step four and five, according to the optimization variables
Figure FDA00034702522000000613
Value setting of linear density variation function of interference fringe
Figure FDA0003470252200000067
Changing cycles according to the second stepThe total exposure of phase scanning photoetching is calculated and obtained
Figure FDA0003470252200000068
Figure FDA00034702522000000615
Corresponding phase error
Figure FDA0003470252200000069
To pair
Figure FDA00034702522000000610
A fourth-order polynomial fitting is performed,
Figure FDA00034702522000000611
is a fitting polynomial of
Figure FDA00034702522000000612
Recording cubic item coefficients
Figure FDA0003470252200000071
Step four and six, according to the optimization variables
Figure FDA0003470252200000072
Value setting of linear density variation function of interference fringe
Figure FDA0003470252200000073
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure FDA0003470252200000074
Figure FDA00034702522000000716
Corresponding phase error
Figure FDA0003470252200000075
To pair
Figure FDA0003470252200000076
A fourth-order polynomial fitting is performed,
Figure FDA0003470252200000077
is a fitting polynomial of
Figure FDA0003470252200000078
Recording cubic item coefficients
Figure FDA0003470252200000079
Step four and seven, if
Figure FDA00034702522000000710
Then
Figure FDA00034702522000000711
Figure FDA00034702522000000712
If not, then,
Figure FDA00034702522000000713
Figure FDA00034702522000000714
step IV, step V, step I m2 ＝i m2 +1, returning to the fourth step and the third step;
step four nine,
Figure FDA00034702522000000715
6. The method for designing the linear density of the aberration-eliminating variable-pitch grating scanning photoetching stripes according to claim 1, characterized in that: the concrete process of the step five is as follows:
step five, obtaining m according to step four 2_optimal Setting the linear density variation function f of the interference fringe 2optimal ＝n g0 +n g1 ·(x-W g /2)+m 2_optimal ·(x-W g /2) 2 +m 3_optimal ·(x-W g /2) 3 Calculating to obtain psi according to the calculation method of the total exposure of the variable-period scanning photoetching given in the step two tot_2optimal Error of phase phi e_2optimal ＝Ψ tot_2optimal -Φ g To phi e_2optimal Performing a fourth order polynomial fit of phi e_2optimal Has a fitting polynomial of phi ep_2optimal (x)＝2π(a 4_2optimal x 4 +a 3_2optimal x 3 +a 2_2optimal x 2 +a 1_2optimal x+a 0_2optimal ) Recording the coefficient of quadratic term a 2_2optimal ；
Quadratic term phase error threshold xi for setting coefficient m1 optimization design of interference fringe linear density change function f (x) 2order ；
Step five and step two, setting the search range [ a ] of iterative optimization m1 (0) ,b m1 (0) ]，a m1 (0) ＝m 1_nearby -H m1 ，b m1 (0) ＝m 1_nearby +H m1 ，2H m1 Is m 1 Breadth of initial search range of optimum value, number of iterations i m1 ＝0，m 1_nearby Is the optimal solution m 1_optimal To an initial approximation of the first,
Figure FDA0003470252200000081
initial quadratic phase error maximum of phi e_2order_m1 (0) ＝abs(2πa 2_2optimal W g 2 )；
Step five and three, if
Figure FDA0003470252200000082
If the threshold value requirement is not met, executing the step five four to five eight, otherwise, exiting the loop and executing the step five nine；
Step five and four, adopting a one-dimensional searching method in
Figure FDA0003470252200000083
Internally determined optimization variables
Figure FDA0003470252200000084
And
Figure FDA0003470252200000085
Figure FDA0003470252200000086
step five, according to the optimization variables
Figure FDA0003470252200000087
Value setting of linear density variation function of interference fringe
Figure FDA0003470252200000088
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure FDA0003470252200000089
Figure FDA00034702522000000829
Corresponding phase error
Figure FDA00034702522000000810
To pair
Figure FDA00034702522000000811
A fourth-order polynomial fitting is performed,
Figure FDA00034702522000000812
is a fitting polynomial of
Figure FDA00034702522000000813
Recording secondary item coefficients
Figure FDA00034702522000000814
Step five and six, according to the optimization variables
Figure FDA00034702522000000815
Value setting of linear density variation function of interference fringe
Figure FDA00034702522000000816
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure FDA00034702522000000817
Figure FDA00034702522000000830
Corresponding phase error
Figure FDA00034702522000000818
To pair
Figure FDA00034702522000000819
A fourth-order polynomial fitting is performed,
Figure FDA00034702522000000820
is a fitting polynomial of
Figure FDA00034702522000000821
Recording secondary item coefficients
Figure FDA00034702522000000822
Step five and seven, if
Figure FDA00034702522000000823
Then the
Figure FDA00034702522000000824
Figure FDA00034702522000000825
If not, then the mobile terminal can be switched to the normal mode,
Figure FDA00034702522000000826
Figure FDA00034702522000000827
step five eight, i m1 ＝i m1 +1, returning to the step five;
the fifth step is,
Figure FDA00034702522000000828
7. The method for designing the linear density of the aberration-eliminating variable-pitch grating scanning photoetching stripes according to claim 1, characterized in that: the concrete process of the step six is as follows:
step six, obtaining m according to step five 1_optimal Setting the linear density variation function f of the interference fringe 1optimal ＝n g0 +m 1_optimal ·(x-W g /2)+m 2_optimal ·(x-W g /2) 2 +m 3_optimal ·(x-W g /2) 3 Calculating to obtain psi according to the calculation method of the total exposure of the variable-period scanning photoetching given in the step two tot_1optimal Error of phase phi e_1optimal ＝Ψ tot_1optimal -Φ g To phi e_1optimal Performing a fourth order polynomial fit of phi e_1optimal Has a fitting polynomial of phi ep_1optimal (x)＝2π(a 4_ 1optimal x 4 +a 3_1optimal x 3 +a 2_1optimal x 2 +a 1_1optimal x+a 0_1optimal ) Recording the coefficient of the primary term a 1_1optimal ；
Setting interference fringesPrimary term phase error threshold xi of coefficient m0 optimization design of linear density variation function f (x) 1order ；
Step six and two, setting a search range [ a ] of iterative optimization m0 (0) ,b m0 (0) ]，a m0 (0) ＝m 0_nearby -H m0 ，b m0 (0) ＝m 0_nearby +H m0 ，2H m0 Is m 0 Width of initial search range of optimum value, number of iterations i m0 ＝0，m 0_nearby Is the optimal solution m 0_optimal Initial approximation of, m 0_nearby ＝n g0 -a 1_1optimal The initial first order phase error maximum is phi e_1order_m0 (0) ＝abs(2πa 1_1optimal W g )；
Step six and three, if
Figure FDA0003470252200000091
If the threshold requirement is not met, executing the steps six four to six eight, otherwise, exiting the circulation and executing the step six nine;
sixthly, adopting a one-dimensional searching method to perform
Figure FDA0003470252200000092
Internally determined optimization variables
Figure FDA0003470252200000093
And
Figure FDA0003470252200000094
Figure FDA0003470252200000095
step six and five, according to the optimization variables
Figure FDA0003470252200000096
Value setting of linear density variation function of interference fringe
Figure FDA0003470252200000097
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure FDA0003470252200000098
Figure FDA00034702522000000916
Corresponding phase error
Figure FDA0003470252200000099
To pair
Figure FDA00034702522000000910
A fourth-order polynomial fitting is performed,
Figure FDA00034702522000000911
is a fitting polynomial of
Figure FDA00034702522000000912
Recording one-time item coefficient
Figure FDA00034702522000000913
Step six, according to the optimization variables
Figure FDA00034702522000000914
Value setting of linear density variation function of interference fringe
Figure FDA00034702522000000915
Calculating according to the method for calculating the total exposure of the variable-period scanning photoetching given in the step two
Figure FDA0003470252200000101
Figure FDA00034702522000001014
Corresponding phase error
Figure FDA0003470252200000102
To pair
Figure FDA0003470252200000103
A fourth-order polynomial fitting is performed,
Figure FDA0003470252200000104
is a fitting polynomial of
Figure FDA0003470252200000105
Recording one-time item coefficient
Figure FDA0003470252200000106
Step six and seven, if
Figure FDA0003470252200000107
Then the
Figure FDA0003470252200000108
Figure FDA0003470252200000109
If not, then,
Figure FDA00034702522000001010
then
Figure FDA00034702522000001011
Figure FDA00034702522000001012
Step six, eight, i m0 ＝i m0 +1, returning to the step five;
sixty nine steps,
Figure FDA00034702522000001013
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2000039359A (en) * 1998-07-23 2000-02-08 Japan Atom Energy Res Inst Conical diffraction oblique incident spectroscope and diffraction grating there for
CN1544994A (en) * 2003-11-26 2004-11-10 中国科学院长春光学精密机械与物理研 Method for accurately controlling density of scribed lines during plane holographic grating fabricating process
CN101793988A (en) * 2009-12-31 2010-08-04 中国科学院长春光学精密机械与物理研究所 Method for accurately adjusting groove density in light path for making holographic grating
CN104297829A (en) * 2014-09-30 2015-01-21 中国科学院长春光学精密机械与物理研究所 Method for optimum design of planar variable-pitch grating
CN105403941A (en) * 2015-12-23 2016-03-16 中国科学技术大学 Near-filed holographic-ion beam etching preparation method of variable-spacing raster
CN111856636A (en) * 2020-07-03 2020-10-30 中国科学技术大学 Variable-pitch grating mask line density distribution controllable fine adjustment method

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP5170488B2 (en) * 2001-07-10 2013-03-27 独立行政法人日本原子力研究開発機構 Conical diffraction oblique incidence spectrometer and diffraction grating for the spectrometer

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2000039359A (en) * 1998-07-23 2000-02-08 Japan Atom Energy Res Inst Conical diffraction oblique incident spectroscope and diffraction grating there for
CN1544994A (en) * 2003-11-26 2004-11-10 中国科学院长春光学精密机械与物理研 Method for accurately controlling density of scribed lines during plane holographic grating fabricating process
CN101793988A (en) * 2009-12-31 2010-08-04 中国科学院长春光学精密机械与物理研究所 Method for accurately adjusting groove density in light path for making holographic grating
CN104297829A (en) * 2014-09-30 2015-01-21 中国科学院长春光学精密机械与物理研究所 Method for optimum design of planar variable-pitch grating
CN105403941A (en) * 2015-12-23 2016-03-16 中国科学技术大学 Near-filed holographic-ion beam etching preparation method of variable-spacing raster
CN111856636A (en) * 2020-07-03 2020-10-30 中国科学技术大学 Variable-pitch grating mask line density distribution controllable fine adjustment method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
扫描干涉场曝光系统中干涉条纹周期测量误差对光栅掩模槽形的影响;姜珊，巴音贺希格，宋莹等;《光学学报》;20140430;第34卷(第4期);第0405003-1-0405003-9页 *
扫描干涉场曝光系统中干涉条纹周期精确测量方法;姜珊，巴音贺希格等;《光学学报》;20150731;第35卷(第7期);第0705001-1-0705001-10页 *

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