CN112784372A - Method and system for calculating gray level graph of curved surface structure processed by focused ion beam - Google Patents
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Abstract
The invention relates to a method and a system for calculating a gray scale diagram of a curved surface structure processed by a focused ion beam. And comparing the simulation contour with the design contour to obtain a contour error, repeatedly screening adaptive parameters in the error general formula by using a genetic algorithm, and finally outputting the optimal ion dose contour by the system and converting the optimal ion dose contour into a corresponding gray-scale image. The machining error general formula provided by the invention can compensate the contour error in a general sense, and has the advantages of low cost and high efficiency.
Description
Technical Field
The invention relates to the technical field of MEMS (micro-electromechanical system) focused ion beam sputter etching processes, in particular to a method and a system for calculating a gray scale map of a curved surface structure processed by a focused ion beam.
Background
The focused ion beam sputtering etching process is an efficient micromachining method, the technology utilizes high-energy ion beams to bombard the surface of a material to sputter the material so as to finish the removal of the material, and the technology has the advantages of simplicity and high efficiency. The required microstructure can be processed by accurately controlling the processing parameters of the ion beam, such as ion beam current, residence time, pixel overlapping rate and the like and setting a reasonable scanning strategy. The gray scale process is often used for processing a three-dimensional microstructure with a complex curved surface, the process integrates the position and time information of an ion beam into a gray scale map (bitmap file), and the milling processing of a focused ion beam is realized by defining the scanning area, the scanning strategy, the pixel overlapping rate and the residence time of each pixel point of the ion beam through the gray scale map file.
After the gray scale image is inputted into the system, the system scans the pixels of the gray scale image one by one, and each processing pass scans all the pixels of the gray scale image once, and usually, the gray scale image is processed for multiple passes to obtain the desired structure. Each pixel in the gray-scale image has a gray value between 0 and 255, and each pixel point comprises three color channels of red, green and blue in RGB coding. The green color of the gray scale determines whether the beam current is empty at the pixel point, and any non-zero pixel value can activate the beam current. The blue channel determines the residence time of the pixel point, the value of the blue channel determines the length of the residence time, when the value of the blue channel is 0, the residence time of the pixel point is 100ns, if the value is set to be 255, the residence time of the pixel point is the residence time set by the user interface, and the residence time corresponding to the pixel point with the blue color value of 0-255 is linear interpolation from the residence time to the maximum value. The gray value of each pixel point is regulated and controlled, and then the ion dose contour of the whole processing area can be controlled.
The traditional grey-scale map is often made according to the proportional relation between the grey-scale value and the processing depth of the pixel point, that is, the depth value of each point of the microstructure is linearly converted into the grey-scale value between 0 and 255. However, due to factors such as the change of the sputtering yield along with the incident angle, the redeposition effect, the beam overlapping effect, and the like, the microstructure processed by using the conventional gray-scale map has a certain error compared with an ideal structure, the actual processing depth of each pixel point in the processing area is often not in proportion to the gray value of the point, and in addition, the shapes of the processing errors are different for curved surface microstructures with different shapes, which brings corresponding difficulty to the determination of the gray value.
In the prior art, a general method capable of generating a corresponding gray scale map of a processed curved surface structure is not developed, and considering that a processing error of a traditional gray scale map has strict correlation with the shape of a preset structure, it is difficult to develop a general method for compensating the processing error and considering the error compensation in the gray scale value calculation.
Disclosure of Invention
The invention provides a method and a system for calculating a gray level map of a curved surface structure processed by a focused ion beam, which can accurately determine the gray level value of each pixel point in the gray level map and carry out targeted correction on processing errors.
The technical scheme adopted by the invention is as follows:
a method for calculating a gray level graph of a curved surface structure processed by a focused ion beam comprises the following steps:
s1: establishing a corresponding error general formula according to the outline form of the preset curved surface structure;
s2: the method comprises the steps of utilizing a focused ion beam gray level process sputtering etching simulation optimization system based on a continuous cellular automaton to realize contour simulation of different times of a gray level process and optimization of process parameters;
s3: converting the optimal ion dose profile output by the system into a corresponding gray scale map;
in S1, starting from the mechanism of error generation in processing a predetermined curved surface structure by a conventional gray scale map (where the default ion dose is linear with the expected depth), in a micro-curved surface structure with continuous derivatives, the processing error tends to occur at a position between two adjacent stagnation points of the designed structure or between a single stagnation point and two sides of the designed structure. This is because at the stagnation point of the curved surface structure, the slope of the point is zero and the ion incident angle is zero, so that the curved surface structure is not excessively etched due to the change of the sputtering yield with the ion beam incident angle, and at the edge position of the microstructure, since the ion dose is gradually reduced, the machining error is also gradually reduced until zero, and considering that the machining error caused by the change of the sputtering yield is represented as excessive cutting, the form of the machining error is gradually increased first and then gradually reduced.
Based on the mechanism of generating focused ion beam sputter etching error, an error general formula F is establishedcompensationComprises the following steps:
wherein a is the length of one side of the processed structure on the coordinate axis; alpha is an error amount control coefficient and controls the magnitude of the error amount; n and c are error shape control coefficients which control the steepness of the error general formula; and x is an independent variable in the error general formula and represents a coordinate value on a machining range, and the value range is [ -a, a ].
In S3, the optimal ion dose profile output by the program is converted into a corresponding gray-scale image, a matrix in the X, Y direction is defined according to the pixel size and the size of the gray-scale image, the value in the height direction is selected, the value is divided by the maximum value in the height direction of the ion dose profile, and then the value is converted into an integer between 0 and 255 to obtain the gray-scale value on the coordinate, and finally the optimized gray-scale image is obtained.
A focused ion beam processing curved surface structure gray level graph calculation system is applied to the calculation method, the system is a focused ion beam gray level process sputtering etching simulation optimization system based on a continuous cellular automaton, and comprises three functional modules which are respectively an initialization module, a contour simulation module and a process parameter optimization module;
the initialization module is used for initializing the input parameters and determining an initial ion dose profile F according to the profile form of the design structureinitialAnd corresponding error general formula FcompensationThe error general formula is used as a correction quantity and is superposed with the initial ion dose profile to obtain a corrected ion dose profile Fmodified：
Fmodified＝Finitial+Fcompensation
After obtaining the corrected ion dose profile, converting the ion dose profile into a two-dimensional ion dose matrix which can be identified by a cellular system:
the contour simulation module is used for realizing contour simulation of different turns of focused ion beam gray level process processing, and the system outputs a final simulation contour according to the simulation turn input by the program;
the process parameter optimization module is used for optimizing the adaptive parameters in the error general formula, comparing the simulation contour in the contour simulation module with the design contour to obtain a contour error, screening the optimal adaptive parameters by using a genetic algorithm according to the contour error, and finally outputting an ideal ion dose contour by a program.
The simulation optimization system adopts a continuous cellular automaton to establish a simulation model, and disperses a simulation space into a series of cellular sets, wherein the cellular space comprises substrate cells (substrate cells) and air cells (vacuum cells), each cell specifies a certain occupation amount to represent the content of substances in the cells, and the conversion function of the cell types is represented as:
in the above formula, C denotes a cell, ω is the maximum value of the occupancy, ρ is the occupancy of the substance in the current cell, and i, j, k are coordinates of the cell in the three-dimensional space. When the substance content in the substrate cell is less than zero, the cell is set as an air cell (Vacuum cell).
The invention has the following beneficial effects:
the invention provides a gray scale map generation method and a gray scale map generation system for processing a preset curved surface microstructure by a focused ion beam gray scale process. According to the mechanism of gray scale process error generation, an error general formula is established, and the general formula can effectively compensate errors generated in processing. The sputter etching simulation optimization system established by the invention corrects the error general formula by comparing and calculating the deviation between the simulation outline and the design outline and utilizing the genetic algorithm, thereby screening out three optimal adaptive parameters in the error general formula, outputting the optimal ion dose outline and obtaining the corresponding gray scale map. Compared with the method for optimizing the gray value in the gray image by repeated experiments, the method and the system for generating the gray image have the advantages of simplicity, easiness in operation, low cost, high efficiency and certain universality.
Drawings
FIG. 1 is a flow chart of a computing method incorporating the computing system of the present invention.
Fig. 2 is a schematic diagram of a gray scale process for a focused ion beam in the prior art.
Fig. 3 is a schematic flow chart of the calculation method of the present invention in which the initial ion dose profile and the error general formula are superimposed to obtain the optimized ion dose profile.
FIG. 4 is a schematic flow chart of the present invention for converting the modified ion dose profile into a two-dimensional ion dose matrix that can be identified by the cellular system in the initialization module of the computing system.
FIG. 5 is a schematic diagram of the conversion process from ion dose profile to gray scale map in the calculation method of the present invention.
Fig. 6 is a graph of simulated etch features using pre-optimization and post-optimization ion dose profiles in accordance with a first embodiment of the present invention.
FIG. 7 is a schematic diagram of an original gray scale map and a processed quadratic parabola structure according to an embodiment of the present invention.
FIG. 8 is a modified gray scale graph and a quadratic parabola structure processed according to an embodiment of the present invention.
Fig. 9 is a simulated etch feature profile using pre-optimization and post-optimization ion dose profiles in accordance with a second embodiment of the present invention.
Fig. 10 is a schematic diagram of an original gray scale map and a cubic parabola structure processed by the original gray scale map according to a second embodiment of the present invention.
Fig. 11 is a modified gray scale and a processed cubic parabola structure according to the second embodiment of the present invention.
Detailed Description
The following describes embodiments of the present invention with reference to the drawings.
The method for calculating the gray level graph of the curved surface structure processed by the focused ion beam comprises the following steps:
the processing target is as follows:
the secondary parabolic curved surface concave structure is 4 mu m in width and 1 mu m in depth;
the targeted optimization object is: and processing a gray scale image corresponding to the quadratic parabolic curved surface concave structure.
As shown in fig. 1, the method comprises the following steps:
s1: according to the form of the quadratic parabolic curved concave structure, as shown in fig. 2, starting from the mechanism of error generation of a conventional gray scale map (default ion dose is linear with expected depth) in processing a preset curved surface structure, in a micro-curved surface structure with continuous derivatives, processing errors tend to occur at positions between two adjacent stagnation points of a designed structure or from a single stagnation point to two sides of the structure. This is because at the stagnation point of the curved surface structure, the slope of the point is zero and the ion incident angle is zero, so that the curved surface structure is not excessively etched due to the change of the sputtering yield with the ion beam incident angle, and at the edge position of the microstructure, since the ion dose is gradually reduced, the machining error is also gradually reduced until zero, and considering that the machining error caused by the change of the sputtering yield is represented as excessive cutting, the form of the machining error is gradually increased first and then gradually reduced.
Based on the mechanism of generating focused ion beam sputter etching error, an error general formula F is establishedcompensationComprises the following steps:
in the formula, a is the range of processing errors: in particular the length of the machined structure on one side of the coordinate axis.
Considering that the designed quadratic parabolic curved surface concave structure is bilaterally symmetrical, the stagnation point of the structure is in the central position, so the compensation range is the range from the middle to the two side edges of the structure, and a is determined to be a single-side range with the length of 2 mu m; alpha is an error amount control coefficient and controls the whole error amount, and N and c are error shape influence coefficients and control the steepness degree of an error general formula; the value range of x is (-2 μm, 2 μm).
S2: establishing a focused ion beam gray level process sputtering etching simulation optimization system based on a continuous cellular automaton, wherein the focused ion beam gray level process sputtering etching simulation optimization system is used for realizing contour simulation of different times of a gray level process and optimization of process parameters;
s3: as shown in fig. 5, the optimal ion dose profile output by the model is converted into a corresponding gray scale map.
The system for calculating the gray scale map of the curved surface structure for processing the focused ion beam in the embodiment, that is, the system established in the calculation method S2, is a focused ion beam gray scale process sputter etching simulation optimization system based on a continuous cellular automaton, as shown in fig. 2 to 4, a simulation space is dispersed into a series of cellular collections, a cellular space includes a base cellular and an air cellular, each cellular defines a certain occupation amount to represent the content of a substance therein, and a conversion function of the cellular type is represented as:
wherein C denotes a cell, ω is a maximum value of the occupancy, ρ is the occupancy of the substance in the current cell, and i, j, k are coordinates of the cell in the three-dimensional space, that is, when the substance content in the substrate cell is less than zero, the cell is set as an air cell (Vacuum cell).
As shown in fig. 1, the simulation optimization system includes three functional modules, which are an initialization module, a profile simulation module, and a process parameter optimization module.
An initialization module for initializing the input parameters and determining an initial ion dose profile F according to the profile form of the design structureinitialAnd corresponding error general formula FcompensationAs shown in FIG. 3, the error formula FcompensationAs correction amount, with the initial ion dose profile FinitialAdding to obtain a corrected ion dose profile Fmodified。
Fmodified＝Finitial+Fcompensation
As shown in FIG. 4, a corrected ion dose profile F is obtainedmodifiedAnd then converting the ion dose matrix into a two-dimensional ion dose matrix which can be identified by a cellular system.
The contour simulation module is used for realizing contour simulation of different turns of focused ion beam gray level process processing, and the system outputs a final simulation contour according to the simulation turn input by the program;
a process parameter optimization module for correcting the error general formula FcompensationThe self-adaptive parameters in (1) are optimized, as shown in fig. 6, the simulation contour in the contour simulation module is compared with the design contour to obtain a contour error, the optimal self-adaptive parameters are screened out by utilizing a genetic algorithm according to the contour error, and finally, an ideal optimal ion dose contour is output by a program.
This example is to improve the error formula FcompensationThe self-adaptability of the method is that the method can adapt to the universal expression of the structural errors of curved surfaces with different aspect ratios, and the general formula of the error F iscompensationThree adaptive coefficients alpha, N, c are set.
The self-adaptive coefficient alpha is related to the aspect ratio of the structure, when the aspect ratio of the processed structure is larger, the generated processing error is larger, so the coefficient alpha is used as a deviation amount control coefficient to control the absolute amount of the error general formula on the height, and when the aspect ratio of the structure is larger, the alpha is also larger; the shape of the machining error is different for different machining structures, the adaptive coefficient N, c is used as a shape influence coefficient, the shape influence coefficient is related to the steepness degree of the structure to be machined, the steepness degree of the error general shape curve is controlled, and when the steepness degree of the machining structure is larger, N, c is also larger. It is worth mentioning that the three coefficients are independent and do not affect each other.
In one embodiment, in the process parameter optimization module, the optimal adaptive parameter is calculated by using a genetic algorithm, and the error general formula F is first calculated according to an initial simulation paircompensationThe value ranges of the three adaptive coefficients in the method are limited, in the example, the range of the adaptive coefficient alpha is 80-120, the range of the adaptive coefficient N is 1.6-2.4, the range of the adaptive coefficient c is 0.8-1.6, then 30 groups of initial population of adaptive parameters are generated in the system, when the maximum iteration times are met, the optimal adaptive coefficient in the error general formula is calculated, the values of alpha and N, c are 105.1, 1.6 and 1.0 respectively, and the optimal ion dose profile is finally output.
The optimized gray scale map is used for processing on FIB equipment, and compared with the processing result of the conventional gray scale map, as shown in FIGS. 7-8.
The method for calculating the gray level graph of the curved surface structure processed by the focused ion beam comprises the following steps:
processing the target: the cubic parabola curved surface concave structure has the width of 4 mu m and the depth of 1 mu m;
optimizing the object: processing gray scale image corresponding to cubic parabola curved surface concave structure
S1: according to the form of the cubic parabola curved surface concave structure, an error general formula is established as follows:
wherein a is the length of one side of the processed structure on the coordinate axis; alpha is an error amount control coefficient and controls the magnitude of the error amount; n and c are error shape control coefficients which control the steepness of the error general formula; x is an independent variable in the error general formula, represents a coordinate value on a processing range, and has a value range of [ -a, a ], considering that the designed cubic parabola curved surface concave structure is bilaterally symmetrical, and the stagnation point of the structure is at the central position, so the compensation range is from the middle to the two side edges of the structure, wherein a is a single-side compensation range and has the length of 2 mu m;
s2: establishing a focused ion beam gray level process sputtering etching simulation optimization system based on a continuous cellular automaton, wherein the focused ion beam gray level process sputtering etching simulation optimization system is used for realizing contour simulation of different times of a gray level process and optimization of process parameters;
s3: and converting the optimal ion dose profile output by the model into a corresponding gray-scale map.
The system for calculating the gray scale map of the curved surface structure for processing the focused ion beam in the embodiment, that is, the system established in the calculation method S2, is a focused ion beam gray scale process sputter etching simulation optimization system based on a continuous cellular automaton, as shown in fig. 2 to 4, a simulation space is dispersed into a series of cellular collections, a cellular space includes a base cellular and an air cellular, each cellular defines a certain occupation amount to represent the content of a substance therein, and a conversion function of the cellular type is represented as:
wherein C denotes a cell, ω is the maximum value of the occupancy, p is the occupancy of the substance in the current cell, i, j, k are the coordinates of the cell in three-dimensional space, i.e. when the substance content in the substrate cell is less than zero, the cell is set as an air cell (Vacuum cell).
As shown in fig. 1, the simulation optimization system includes three functional modules, which are an initialization module, a profile simulation module, and a process parameter optimization module.
An initialization module for initializing the input parameters and determining an initial ion dose profile F according to the profile form of the design structureinitialAnd corresponding error general formula FcompensationError general formula FcompensationAs correction amount, with the initial ion dose profile FinitialAdding to obtain a corrected ion dose profile Fmodified。
Fmodified＝Finitial+Fcompensation
Obtaining a corrected ion dose profile FmodifiedAnd then converting the ion dose matrix into a two-dimensional ion dose matrix which can be identified by a cellular system.
The contour simulation module is used for realizing contour simulation of different turns of focused ion beam gray level process processing, and the system outputs a final simulation contour according to the simulation turn input by the program;
a process parameter optimization module for correcting the error general formula FcompensationThe self-adaptive parameters in (1) are optimized, as shown in fig. 9, the simulation contour in the contour simulation module is compared with the design contour to obtain a contour error, the optimal self-adaptive parameters are screened out by using a genetic algorithm according to the contour error, and finally, an ideal optimal ion dose contour is output by a program.
This embodiment is to improveError general formula FcompensationThe self-adaptability of the method is that the method can adapt to the universal expression of the structural errors of curved surfaces with different aspect ratios, and the general formula of the error F iscompensationThree adaptive coefficients alpha, N, c are set.
The self-adaptive coefficient alpha is related to the aspect ratio of the structure, when the aspect ratio of the processed structure is larger, the generated processing error is larger, so the coefficient alpha is used as a deviation amount control coefficient to control the absolute amount of the error general formula on the height, and when the aspect ratio of the structure is larger, the alpha is also larger; the shape of the machining error is different for different machining structures, the adaptive coefficient N, c is used as a shape influence coefficient, the shape influence coefficient is related to the steepness degree of the structure to be machined, the steepness degree of the error general shape curve is controlled, and when the steepness degree of the machining structure is larger, N, c is also larger. It is worth mentioning that the three coefficients are independent and do not affect each other.
As an implementation manner, in the process parameter optimization module, the optimal adaptive parameters are calculated by using a genetic algorithm, the value ranges of three adaptive coefficients in the error general formula are limited according to an initial simulation, in this example, the range of the adaptive coefficient α is 100 to 160, the range of the adaptive coefficient N is 1.8 to 3.0, and the range of the adaptive coefficient c is 1.2 to 2.0, then 30 sets of initial populations of the adaptive parameters are generated in the system, when the maximum iteration number is satisfied, the optimal adaptive coefficients in the error general formula are calculated, where α and N, c are 140, 2.576, and 1.572, respectively, and finally the optimal ion dose profile is output.
The optimized gray scale map is used for processing on FIB equipment, and compared with the processing result of the conventional gray scale map, as shown in FIGS. 10-11.
Claims (4)
1. A method for calculating a gray level graph of a curved surface structure processed by a focused ion beam is characterized by comprising the following steps:
s1: establishing a corresponding error general formula according to the outline form of the preset curved surface structure;
s2: the method comprises the steps of utilizing a focused ion beam gray level process sputtering etching simulation optimization system based on a continuous cellular automaton to realize contour simulation of different times of a gray level process and optimization of process parameters;
s3: converting the optimal ion dose profile output by the system into a corresponding gray scale map;
in the step S1, an error general formula F is established based on the mechanism that the error of the preset curved surface structure processed by the traditional gray scale image is generatedcompensationComprises the following steps:
wherein a is the length of one side of the processed structure on the coordinate axis; alpha is an error amount control coefficient and controls the magnitude of the error amount; n and c are error shape control coefficients which control the steepness of the error general formula; and x is an independent variable in the error general formula and represents a coordinate value on a machining range, and the value range is [ -a, a ].
2. The method as claimed in claim 1, wherein in step S3, the optimal ion dose profile outputted by the program is converted into a corresponding gray scale image, a matrix in the X, Y direction is defined according to the pixel size and the gray scale image size, the value in the height direction is selected and divided by the maximum value in the height of the ion dose profile, and then the matrix is converted into an integer between 0 and 255 to obtain the gray scale value in the coordinate, thereby obtaining the optimized gray scale image.
3. A system for calculating a gray scale map of a curved surface structure processed by a focused ion beam is characterized by being applied to the calculation method of claim 1, wherein the system is a focused ion beam gray scale process sputtering etching simulation optimization system based on a continuous cellular automaton, and comprises three functional modules which are respectively an initialization module, a contour simulation module and a process parameter optimization module;
the initialization module is used for initializing the input parameters and determining an initial ion dose profile F according to the profile form of the design structureinitialAnd corresponding error general formulaFcompensationThe error general formula is used as a correction quantity and is superposed with the initial ion dose profile to obtain a corrected ion dose profile Fmodified：
Fmodified＝Finitial+Fcompensation
After the corrected ion dose profile is obtained, converting the ion dose profile into a two-dimensional ion dose matrix which can be identified by a cellular system;
the contour simulation module is used for realizing contour simulation of different turns of focused ion beam gray level process processing, and the system outputs a final simulation contour according to the simulation turn input by the program;
the process parameter optimization module is used for optimizing the adaptive parameters in the error general formula, comparing the simulation contour in the contour simulation module with the design contour to obtain a contour error, screening the optimal adaptive parameters by using a genetic algorithm according to the contour error, and finally outputting an ideal ion dose contour by a program.
4. The system of claim 3, wherein the simulation optimization system uses a continuous cellular automaton to build a simulation model, and discretizes a simulation space into a series of cell sets, the cell space includes a substrate cell (substrate cell) and an air cell (vacuum cell), each cell specifies a certain occupancy amount to represent the material content therein, and the conversion function of the cell type is represented as:
in the above formula, C denotes a cell, ω is the maximum value of the occupancy, ρ is the occupancy of the substance in the current cell, and i, j, k are coordinates of the cell in the three-dimensional space.
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| CN111738397A (en) * | 2020-06-17 | 2020-10-02 | 江苏师范大学 | NURBS curve fitting method based on genetic particle swarm optimization |
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| CN109165400A (en) * | 2018-07-06 | 2019-01-08 | 东南大学 | A kind of design method of focused-ion-beam lithography working process parameter |
| CN110781590A (en) * | 2019-10-18 | 2020-02-11 | 武汉数字化设计与制造创新中心有限公司 | Gray scale map generation method and system for processing three-dimensional microstructure by FIBM |
| CN111738397A (en) * | 2020-06-17 | 2020-10-02 | 江苏师范大学 | NURBS curve fitting method based on genetic particle swarm optimization |
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