CN110543655A - optimal design method and device for precision alignment platform of nano-imprinting equipment - Google Patents
optimal design method and device for precision alignment platform of nano-imprinting equipment Download PDFInfo
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Abstract
the invention discloses an optimal design method and device for a precision alignment platform of nanoimprint equipment, wherein the method comprises the following steps: acquiring a parallel mechanism meeting design requirements; performing optimization calculation on the structural parameters of the parallel mechanism to obtain the optimal structural parameters of the parallel mechanism; calculating an optimal input and output mapping matrix according to the optimal structure parameters, and obtaining an expected mapping matrix after correction; performing optimization solution on a preset topological optimization model according to optimization constraints to obtain a precision alignment platform unit density distribution map; and finally, drawing a boundary line of the unit density distribution diagram to obtain a precision alignment platform processing model surrounded by the boundary line. By implementing the invention, the precision alignment platform meeting the precision requirement can be prepared, thereby effectively improving the positioning precision of the precision alignment platform of the nano-imprint lithography equipment and enhancing the parallelism adjustment capability of the precision alignment platform.
Description
Technical Field
The invention relates to the technical field of nanoimprint lithography, in particular to an optimal design method and device for a precision alignment platform of nanoimprint lithography equipment.
Background
the nano-imprint technology is a method for realizing batch nano-pattern replication by utilizing stamp transfer printing, and compared with ultraviolet lithography and electron beam lithography, the nano-imprint technology has the processing resolution only related to the size of a template pattern and is not physically limited by the shortest exposure wavelength of lithography. In the nano-imprinting technology, alignment is one of key technologies influencing imprinting precision, and a proper precision positioning platform can realize uniform contact between a template and a substrate and can ensure the positioning precision between the template and the substrate. The existing alignment platform is mostly composed of a servo motor, a lead screw and other mechanisms, and due to the influence of the assembly precision among rigid mechanisms, the alignment platform with the structure cannot be continuously lifted after reaching a certain positioning precision. In order to solve the problem of positioning bottleneck caused by a rigid mechanism, researchers design various precision alignment platforms with self-adaptive template posture change capability based on a self-adaptive principle, the platforms apply imprinting force on a substrate in an imprinting process, and the alignment platforms passively adapt to the posture of a template through self flexibility, but the positioning accuracy is low and the parallelism adjustment capability is weak.
Disclosure of Invention
the technical problem to be solved by the embodiments of the present invention is to provide an optimal design method and apparatus for a precision alignment platform of a nanoimprint lithography apparatus, which can prepare a precision alignment platform meeting precision requirements, thereby effectively improving the positioning precision of the alignment platform of the nanoimprint lithography apparatus and enhancing the parallelism adjustment capability thereof.
In order to solve the above technical problems, the present invention provides an optimized design method for a precision alignment stage of a nanoimprint apparatus, including:
acquiring a parallel prototype mechanism meeting design requirements; wherein the design requirement includes a characteristic that the parallel prototype mechanism is required to have planar three-degree-of-freedom motion;
Performing optimization calculation on the structural parameters of the parallel prototype mechanism according to a preset actual optimization target to obtain the optimal structural parameters of the parallel prototype mechanism;
calculating an optimal input and output mapping matrix according to the optimal structure parameters, and correcting the optimal input and output mapping matrix according to a preset correction coefficient to obtain an expected mapping matrix;
taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as optimization constraint, and performing optimization solution on a preset topological optimization model to obtain a precision alignment platform unit density distribution map;
And drawing boundary lines on the precision alignment platform unit density distribution diagram according to a preset unit density permission threshold value to obtain a precision alignment platform processing model surrounded by the boundary lines.
Further, the design requirements further include requiring the parallel prototype mechanism to be a sliding pair as an active pair.
further, the preset actual optimization target is to maximize the working space of the parallel mechanism or maximize the load of the parallel mechanism.
further, the preset topology optimization model construction method includes:
and taking the kinematic characteristics of the mechanism as an optimization design target, taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as an optimization constraint, and establishing the topological optimization model by adopting an SIMP method in a topological optimization method.
Further, the preset topology optimization model is as follows:
find x＝(x,x,...,x)
max f
V/V≤f
F＝KU
J·U＝U
E＝J-J≤m
wherein xe is a unit density, n is a total number of units in a design domain, Er is a difference value between an input/output mapping matrix and a given expected mapping matrix in a design process, fHz is a low-order modal frequency of the compliant mechanism, Ee is a young modulus of a unit E, Emin and E0 are unit young moduli when the unit densities are 0 and 1 respectively, p is a penalty factor, V is a compliant mechanism permitted volume, V0 is a compliant mechanism initial design area volume, fv is a volume fraction, F is an external force borne by the mechanism, K is a mechanism global stiffness, U is a mechanism global displacement, J is an input/output mapping matrix, Uin and Uout are displacements of a mechanism driving end and an output point respectively, x direction represents a driving freedom direction, y direction represents a direction perpendicular to x, λ is a ratio of two stiffness of an input end, and J is an expected mapping matrix, m is the allowable error between the actual mapping matrix and the expected mapping matrix.
in order to solve the same technical problem, the invention also provides an optimization design device of a precision alignment platform for the nanoimprint equipment, which comprises a parallel mechanism acquisition module, a structural parameter calculation module, a mapping matrix calculation module, a unit density calculation module and an alignment platform model drawing module; wherein the content of the first and second substances,
The parallel mechanism acquisition module is used for acquiring a parallel prototype mechanism meeting the design requirement; wherein the design requirement includes a characteristic that the parallel prototype mechanism is required to have planar three-degree-of-freedom motion;
The structural parameter calculation module is used for carrying out optimization calculation on the structural parameters of the parallel prototype mechanism according to a preset actual optimization target to obtain the optimal structural parameters of the parallel prototype mechanism;
The mapping matrix calculation module is used for calculating an optimal input and output mapping matrix according to the optimal structure parameters and correcting the optimal input and output mapping matrix according to a preset correction coefficient to obtain an expected mapping matrix;
The unit density calculation module is used for taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as optimization constraint, and performing optimization solution on a preset topological optimization model to obtain a unit density distribution map of the precision alignment platform;
and the alignment platform model drawing module is used for drawing boundary lines of the precision alignment platform unit density distribution diagram according to a preset unit density permission threshold value to obtain a precision alignment platform processing model surrounded by the boundary lines.
further, the design requirements further include requiring the parallel prototype mechanism to be a sliding pair as an active pair.
further, the preset actual optimization target is to maximize the working space of the parallel mechanism or maximize the load of the parallel mechanism.
Further, the preset topology optimization model construction method includes:
and taking the kinematic characteristics of the mechanism as an optimization design target, taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as an optimization constraint, and establishing the topological optimization model by adopting an SIMP method in a topological optimization method.
further, the preset topology optimization model is as follows:
find x＝(x,x,...,x)
max f
V/V≤f
F＝KU
J·U＝U
E＝J-J≤m
wherein xe is a unit density, n is a total number of units in a design domain, Er is a difference value between an input/output mapping matrix and a given expected mapping matrix in a design process, fHz is a low-order modal frequency of the compliant mechanism, Ee is a young modulus of a unit E, Emin and E0 are unit young moduli when the unit densities are 0 and 1 respectively, p is a penalty factor, V is a compliant mechanism permitted volume, V0 is a compliant mechanism initial design area volume, fv is a volume fraction, F is an external force borne by the mechanism, K is a mechanism global stiffness, U is a mechanism global displacement, J is an input/output mapping matrix, Uin and Uout are displacements of a mechanism driving end and an output point respectively, x direction represents a driving freedom direction, y direction represents a direction perpendicular to x, λ is a ratio of two stiffness of an input end, and J is an expected mapping matrix, m is the allowable error between the actual mapping matrix and the expected mapping matrix.
compared with the prior art, the invention has the following beneficial effects:
the invention provides an optimization design method and device for a precision alignment platform of nanoimprint lithography equipment, which are used for obtaining a unit density distribution map of each unit in a precision alignment platform design area by a topological optimization method based on mapping matrix constraint, finally extracting a side line of the precision alignment platform according to the obtained unit density distribution map of the precision alignment platform, and preparing the precision alignment platform meeting the precision requirement after processing, thereby effectively improving the positioning precision of the precision alignment platform of the nanoimprint lithography equipment and enhancing the parallelism adjustment capability of the precision alignment platform.
drawings
FIG. 1 is a schematic flow chart of a method for optimizing design of a precision alignment stage for a nanoimprinting apparatus according to an embodiment of the present invention;
Fig. 2 is a schematic structural diagram of a parallel prototype mechanism according to an embodiment of the present invention;
FIG. 3 is a flowchart of an algorithm search for searching for optimal structural parameters of a parallel mechanism according to an embodiment of the present invention;
FIG. 4 is an initial optimized design region of a precision alignment platform according to an embodiment of the present invention;
FIG. 5 is a graph illustrating a density distribution of the fine alignment stage units after optimization according to an embodiment of the present invention;
Fig. 6 is a schematic diagram of a precision alignment stage processing model obtained by extracting edge lines according to a precision alignment stage unit density distribution diagram according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
referring to fig. 1, an embodiment of the present invention provides a method for optimally designing a precision alignment stage of a nanoimprinting apparatus, including:
step S1, acquiring a parallel prototype mechanism meeting the design requirement; wherein the design requirement includes a characteristic that the parallel prototype mechanism is required to have planar three-degree-of-freedom motion;
Step S2, performing optimization calculation on the structural parameters of the parallel prototype mechanism according to a preset actual optimization target to obtain the optimal structural parameters of the parallel prototype mechanism;
step S3, calculating an optimal input and output mapping matrix according to the optimal structure parameters, and correcting the optimal input and output mapping matrix according to a preset correction coefficient to obtain an expected mapping matrix;
Step S4, taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as optimization constraint, and carrying out optimization solution on a preset topological optimization model to obtain a precision alignment platform unit density distribution map;
And step S5, drawing boundary lines of the precision alignment platform unit density distribution diagram according to a preset unit density permission threshold value, and obtaining a precision alignment platform processing model surrounded by the boundary lines.
In order to overcome the problems in the background art and enable the input and output of the obtained precision alignment platform to have a given mapping relation, the invention provides an optimization design method of the precision alignment platform for the nano-imprint lithography equipment.
In a preferred embodiment, the design requirements further include requiring the parallel prototyping mechanism to have a sliding pair as the active pair.
in a preferred embodiment, the preset actual optimization objective is to maximize the parallel mechanism working space or maximize the parallel mechanism load.
In a preferred embodiment, the method for constructing the preset topology optimization model includes:
And taking the kinematic characteristics of the mechanism as an optimization design target, taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as an optimization constraint, and establishing the topological optimization model by adopting an SIMP method in a topological optimization method.
in a preferred embodiment, the preset topology optimization model is:
Wherein xe is a unit density, n is a total number of units in a design domain, Er is a difference value between an input/output mapping matrix and a given expected mapping matrix in a design process, fHz is a low-order modal frequency of the compliant mechanism, Ee is a young modulus of a unit E, Emin and E0 are unit young moduli when the unit densities are 0 and 1 respectively, p is a penalty factor, V is a compliant mechanism permitted volume, V0 is a compliant mechanism initial design area volume, fv is a volume fraction, F is an external force borne by the mechanism, K is a mechanism global stiffness, U is a mechanism global displacement, J is an input/output mapping matrix, Uin and Uout are displacements of a mechanism driving end and an output point respectively, x direction represents a driving freedom direction, y direction represents a direction perpendicular to x, λ is a ratio of two stiffness of an input end, and J is an expected mapping matrix, m is the allowable error between the actual mapping matrix and the expected mapping matrix.
in the embodiment of the invention, the optimal structure of the parallel mechanism with the same freedom of movement as that of the precision alignment platform required to be designed is determined.
It can be understood that the parallel mechanism has the advantages of high motion precision, good bearing capacity and the like, and an alignment platform applied to the nano-suppression lithography equipment needs to realize three degrees of freedom including two movements in an XOY plane and rotation around a Z axis, so that the parallel mechanism obtained by searching can realize planar three-degree-of-freedom motion. Meanwhile, the motion precision of the alignment platform in three motion degrees of freedom is ensured, so that the input driving precision of the alignment platform is greatly required. Therefore, the piezoelectric ceramic with ultrahigh resolution is suitable for being input drive of a precision alignment platform, so that a moving pair is required to be an active pair when a parallel mechanism is selected, and the rest moving pairs are not limited;
After finding the corresponding parallel mechanism, the structural parameters of the parallel mechanism, such as the working space and the load of the mechanism, need to be optimized according to the actual situation. In a preferred embodiment of the present invention, a genetic algorithm may be adopted to find the optimal structure parameter meeting the maximum working space of the parallel mechanism in all possible parameter domains of the parallel mechanism, and the input/output mapping matrix of the parallel mechanism at this time is obtained by calculation according to the optimal structure parameter.
it should be noted that, because the parallel prototype mechanism and the compliant mechanism have different transfer motion modes, the compliant mechanism has no obvious kinematic pair and cannot realize large-amplitude rotation, so that the mapping matrix obtained by the parallel prototype mechanism needs to be reasonably corrected, and the corrected mapping matrix is used as an expected mapping matrix in the process of topology optimization of the precision alignment platform. It can be appreciated that the compliant mechanism design parameters (desired mapping matrix) in embodiments of the present invention are derived based on a parallel prototype mechanism.
In the design process of the compliant mechanism, a compliant mechanism optimization model is established by adopting a SIMP method in a topological optimization method, so that the precise alignment platform has better motion characteristics, the mechanism kinematics characteristics are taken as an optimization design target, the difference value between an actual mapping matrix and an expected mapping matrix of the mechanism is taken as optimization constraint, and the initial model of the precise alignment platform (the unit density distribution map of the alignment platform) is obtained by optimization solution.
And finally, obtaining a unit density distribution diagram of each unit in the design area of the precision alignment platform by a topological optimization method, drawing a boundary line containing all permitted unit densities by using a precision alignment platform unit density permission threshold value in the diagram, wherein the area surrounded by the boundary line is the precision alignment platform model which can be used for actual processing and manufacturing.
in the following, a preferred embodiment is listed in conjunction with fig. 2-6 to clearly and completely describe the technical solution of the present invention.
In the embodiment of the invention, the precision alignment platform has three freedom degrees of motion, so that the parallel mechanism to be searched can realize planar three-freedom-degree motion, the moving pair is an active pair, and a planar 3-PRR parallel mechanism is selected as a parallel prototype mechanism of the precision alignment platform, the structural diagram of the parallel prototype mechanism is shown in figure 2, and the parallel mechanism consists of three parts: the movable platform A1A2A3, the fixed platform C1C2C3 and three branched chains AiBiCi (i is 1,2 and 3) connecting the two platforms, and each branched chain comprises two revolute pairs (R) and a moving pair (P).
in the mechanism, the movable platform is a regular triangle with a side length of a (the radius of a circumscribed circle is e), a rectangular coordinate system as shown in fig. 2 is established at the center of the triangle, and three branched chains are symmetrical about an origin of coordinates, wherein the length BiCi of the moving pair is li, and the length AiBi of a connecting rod between the moving pair and the movable platform is bi. For the branched chain A1B1C1, the positional relationship of each point in the plane can be found as follows:
After the mechanism moves, the state of the branched chain A1B1C1 changes correspondingly, and in the process, the elongation of the sliding pair in the branched chain is delta l1, the displacement of the center point o of the movable platform is delta x and delta y, and the rod length and the relative position relation are substituted into the formula (1) to obtain:
because the precision alignment platform is applied to the occasion with small range and high precision, the motion stroke of the precision alignment platform is micron (or submicron) grade, and the size of the precision alignment platform is far smaller than the size of the mechanism, sin delta theta is approximately equal to delta theta, cos delta theta is approximately equal to 1, and the precision alignment platform can be obtained by the formula (2):
Elimination of Δ θ 1, there are:
similarly, the following equations hold for the branched chains A2B2C3, A3B3C 3:
the input/output mapping matrix Jc obtained from equations (4) and (5) is:
in the formula, γ 2 is an angle between the mobile pair P2 in the branched chain A2B2C2 and the horizontal direction, and γ 3 is an angle between the mobile pair P3 in the branched chain A3B3C3 and the horizontal direction, and since three branched chains of the parallel prototype mechanism are symmetrical with respect to the origin of coordinates, γ 2 is-120 °, and γ 3 is 120 °.
the invention adopts the piezoelectric ceramics as the precise alignment platform for driving, and the output displacement of the piezoelectric ceramics is the ith piezoelectric ceramics movement stroke. As shown in equation (7), when the input displacement of the piezoelectric ceramic is equal, the movable platform has the maximum displacement in the degree of freedom j (j is 1,2,3), and when the input displacement of the piezoelectric ceramic is equal, the movable platform has the minimum displacement in the degree of freedom j (j is 1,2,3)
The motion range of the parallel mechanism moving platform in the degree of freedom j (j is 1,2,3) is as follows:
Because the output displacement Uout and the input displacement uin of the parallel mechanism movable platform are in a linear relation, and the value of the sum is selected in the sum of 0 according to the sign of Jc, the formula (8) can be rewritten as follows:
as can be seen from equation (9), the operating range of Uout in the degree of freedom j (j is 1,2,3) is determined by the sum of the absolute values of the mapping matrix elements, and therefore, when the sum of the absolute values of the jth row of the mapping matrix is the largest, the operating range of the parallel mechanism moving platform in the direction of the degree of freedom j is the largest. The embodiment of the invention adopts a genetic algorithm, the maximum fitness function is the multiplication of the square sum of elements of each row of a mapping matrix, a calculation flow chart is shown in figure 3, and the specific step-by-step flow is as follows:
1. Initializing structural parameters of a parallel mechanism; specifically, a parameter value of a unit is selected from all possible parameter domains of the parallel mechanism, and the parameter value comprises an included angle theta i (i is 1,2 and 3) between a branched chain and a horizontal line, a radius e of a circumscribed circle of a movable platform and an initial rotation angle of the movable platform around a coordinate Z axis
2. Calculating the parameter range of the parallel mechanism; respectively calculating the maximum movement displacement and the minimum movement displacement of the parallel mechanism under three degrees of freedom according to the mapping matrix calculated by the current mechanism parameters and the movement stroke of the mapping matrix and the driver to obtain the working range of the current parallel mechanism;
3. sequencing to obtain current optimal structure parameters; the working ranges of the parallel mechanisms under several groups of mechanism parameters can be obtained from the step 1 and the step 2, the working ranges of the mechanisms are sequentially ordered, and the structural parameter when the working space of the mechanism is maximum is taken as the current optimal structural parameter;
4. Judging whether the operation is finished or not; giving the maximum iteration step number of the genetic algorithm, judging whether the current iteration step number is the last iteration step number, if not, performing genetic operations such as selection, crossing, variation and the like on the mechanism parameters to obtain new parallel mechanism structure parameters;
5. Repeating the 2,3 and 4 steps of operation on the parallel mechanism parameters obtained by genetic operation until the maximum iteration step number is reached (preferably, the maximum iteration step number is set to be 500 in the embodiment of the invention);
6. and taking the structural parameter when the working space of the mechanism is maximum as the optimal structural parameter of the parallel mechanism and outputting the optimal structural parameter to obtain the parameter value of the parallel mechanism under the maximum requirement of the working range.
through 500 iterations, the mechanism parameters when the motion space of the parallel mechanism is maximum are obtained, and at the moment, the mechanism structure parameters are respectively: θ 1 is 50 °, θ 2 is-70 °, θ 3 is-130 °, e is 15, and the input/output mapping matrix Jc at this time is:
then, the above-mentioned topological optimization model (a) is established as a precision alignment platform optimization model, in this embodiment, the motion range of the obtained precision alignment platform is required to be 80 μm Δ x, and 80 μm Δ y, according to the maximum driving displacement of the piezoelectric ceramic in the embodiment, the correction Jc manner is 1/100 that is mapped to the component of the Z-axis rotating element to obtain the original value, the remaining components are unchanged, an expected mapping matrix J of the precision alignment platform is obtained, and an optimization design area of the precision alignment platform is set (as shown in fig. 4), where ai (i ═ 1,2,3) is a driving input point, o is a center point of the precision alignment platform, and the triangular area is the precision alignment platform moving platform. Let fv be 0.3 and λ be 30, and the optimization calculation yields the density distribution map of each cell in the design region as shown in fig. 5.
it should be noted that fv represents the percentage of the final desired fine alignment stage volume relative to the initial design area volume of the fine alignment stage shown in fig. 4, and in this embodiment, the final desired fine alignment stage volume is not too large, so that 0.3 of the design area may be used as the desired volume fraction. The value of fv can be any number between (0,1) according to the design will of the designer. λ represents the ratio of the displacement in the driving direction to the displacement in the direction perpendicular to the driving direction. In the present embodiment, since the precision alignment stage is driven by using the piezoelectric ceramics, the displacement of the driving input terminal thereof is 27 μm at the maximum, and for this reason, it is required that the displacement perpendicular to the driving direction is less than 1 μm when the driving direction displacement reaches the maximum, and therefore, λ may be set to 30. In practical application, if different requirements are imposed on the motion range of the precision alignment platform, the correction coefficient of the mapping matrix can be set according to actual requirements.
And extracting a side line of the precision alignment platform according to the obtained density distribution map of the precision alignment platform unit to obtain a precision alignment platform processing model shown in fig. 6, and reasonably installing the platform after actual processing and manufacturing to realize an expected motion track.
It should be noted that the above method or flow embodiment is described as a series of acts or combinations for simplicity, but those skilled in the art should understand that the present invention is not limited by the described acts or sequences, as some steps may be performed in other sequences or simultaneously according to the present invention. Further, those skilled in the art will appreciate that the embodiments described in the specification are exemplary embodiments and that no single embodiment is necessarily required by the inventive embodiments.
In order to solve the same technical problem, the invention also provides an optimization design device of a precision alignment platform for the nanoimprint equipment, which comprises a parallel mechanism acquisition module, a structural parameter calculation module, a mapping matrix calculation module, a unit density calculation module and an alignment platform model drawing module; wherein the content of the first and second substances,
the parallel mechanism acquisition module is used for acquiring a parallel prototype mechanism meeting the design requirement; wherein the design requirement includes a characteristic that the parallel prototype mechanism is required to have planar three-degree-of-freedom motion;
the structural parameter calculation module is used for carrying out optimization calculation on the structural parameters of the parallel prototype mechanism according to a preset actual optimization target to obtain the optimal structural parameters of the parallel prototype mechanism;
the mapping matrix calculation module is used for calculating an optimal input and output mapping matrix according to the optimal structure parameters and correcting the optimal input and output mapping matrix according to a preset correction coefficient to obtain an expected mapping matrix;
the unit density calculation module is used for taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as optimization constraint, and performing optimization solution on a preset topological optimization model to obtain a unit density distribution map of the precision alignment platform;
and the alignment platform model drawing module is used for drawing boundary lines of the precision alignment platform unit density distribution diagram according to a preset unit density permission threshold value to obtain a precision alignment platform processing model surrounded by the boundary lines.
further, the design requirements further include requiring the parallel prototype mechanism to be a sliding pair as an active pair.
Further, the preset actual optimization target is to maximize the working space of the parallel mechanism or maximize the load of the parallel mechanism.
Further, the preset topology optimization model construction method includes:
And taking the kinematic characteristics of the mechanism as an optimization design target, taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as an optimization constraint, and establishing the topological optimization model by adopting an SIMP method in a topological optimization method.
Further, the preset topology optimization model is as follows:
find x＝(x,x,...,x)
max f
V/V≤f
F＝KU
J·U＝U
E＝J-J≤m
wherein xe is a unit density, n is a total number of units in a design domain, Er is a difference value between an input/output mapping matrix and a given expected mapping matrix in a design process, fHz is a low-order modal frequency of the compliant mechanism, Ee is a young modulus of a unit E, Emin and E0 are unit young moduli when the unit densities are 0 and 1 respectively, p is a penalty factor, V is a compliant mechanism permitted volume, V0 is a compliant mechanism initial design area volume, fv is a volume fraction, F is an external force borne by the mechanism, K is a mechanism global stiffness, U is a mechanism global displacement, J is an input/output mapping matrix, Uin and Uout are displacements of a mechanism driving end and an output point respectively, x direction represents a driving freedom direction, y direction represents a direction perpendicular to x, λ is a ratio of two stiffness of an input end, and J is an expected mapping matrix, m is the allowable error between the actual mapping matrix and the expected mapping matrix.
It can be understood that the above apparatus item embodiments correspond to the method item embodiments of the present invention, and the optimal design apparatus for a precision alignment platform of a nanoimprinting apparatus provided in the embodiments of the present invention can implement the optimal design method for a precision alignment platform of a nanoimprinting apparatus provided in any one of the method item embodiments of the present invention.
compared with the prior art, the invention has the following beneficial effects:
The invention provides an optimization design method and device for a precision alignment platform of nanoimprint lithography equipment, which are used for obtaining a unit density distribution map of each unit in a precision alignment platform design area by a topological optimization method based on mapping matrix constraint, finally extracting a side line of the precision alignment platform according to the obtained unit density distribution map of the precision alignment platform, and preparing the precision alignment platform meeting the precision requirement after processing, thereby effectively improving the positioning precision of the precision alignment platform of the nanoimprint lithography equipment and enhancing the parallelism adjustment capability of the precision alignment platform.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.
Claims (10)
1. A method for optimally designing a precision alignment stage for a nanoimprinting apparatus, comprising:
acquiring a parallel prototype mechanism meeting design requirements; wherein the design requirement includes a characteristic that the parallel prototype mechanism is required to have planar three-degree-of-freedom motion;
Performing optimization calculation on the structural parameters of the parallel prototype mechanism according to a preset actual optimization target to obtain the optimal structural parameters of the parallel prototype mechanism;
Calculating an optimal input and output mapping matrix according to the optimal structure parameters, and correcting the optimal input and output mapping matrix according to a preset correction coefficient to obtain an expected mapping matrix;
Taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as optimization constraint, and performing optimization solution on a preset topological optimization model to obtain a precision alignment platform unit density distribution map;
and drawing boundary lines on the precision alignment platform unit density distribution diagram according to a preset unit density permission threshold value to obtain a precision alignment platform processing model surrounded by the boundary lines.
2. The method of claim 1, wherein the design requirements further include requiring the parallel prototype mechanism to be a moving pair as an active pair.
3. The method of claim 1, wherein the pre-set actual optimization objective is to maximize the parallel mechanism working space or maximize the parallel mechanism load.
4. the method of claim 1, wherein the method for constructing the pre-designed topology optimization model comprises:
And taking the kinematic characteristics of the mechanism as an optimization design target, taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as an optimization constraint, and establishing the topological optimization model by adopting an SIMP method in a topological optimization method.
5. the method of claim 1, wherein the preset topology optimization model is:
find x＝(x,x,...,x)
max f
V/V≤f
F＝KU
J·U＝U
E＝J-J≤m
Wherein xe is a unit density, n is a total number of units in a design domain, Er is a difference value between an input/output mapping matrix and a given expected mapping matrix in a design process, fHz is a low-order modal frequency of the compliant mechanism, Ee is a young modulus of a unit E, Emin and E0 are unit young moduli when the unit densities are 0 and 1 respectively, p is a penalty factor, V is a compliant mechanism permitted volume, V0 is a compliant mechanism initial design area volume, fv is a volume fraction, F is an external force borne by the mechanism, K is a mechanism global stiffness, U is a mechanism global displacement, J is an input/output mapping matrix, Uin and Uout are displacements of a mechanism driving end and an output point respectively, x direction represents a driving freedom direction, y direction represents a direction perpendicular to x, λ is a ratio of two stiffness of an input end, and J is an expected mapping matrix, m is the allowable error between the actual mapping matrix and the expected mapping matrix.
6. an optimization design device for a precision alignment platform of nanoimprint equipment is characterized by comprising a parallel mechanism acquisition module, a structural parameter calculation module, a mapping matrix calculation module, a unit density calculation module and an alignment platform model drawing module; wherein the content of the first and second substances,
the parallel mechanism acquisition module is used for acquiring a parallel prototype mechanism meeting the design requirement; wherein the design requirement includes a characteristic that the parallel prototype mechanism is required to have planar three-degree-of-freedom motion;
the structural parameter calculation module is used for carrying out optimization calculation on the structural parameters of the parallel prototype mechanism according to a preset actual optimization target to obtain the optimal structural parameters of the parallel prototype mechanism;
the mapping matrix calculation module is used for calculating an optimal input and output mapping matrix according to the optimal structure parameters and correcting the optimal input and output mapping matrix according to a preset correction coefficient to obtain an expected mapping matrix;
the unit density calculation module is used for taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as optimization constraint, and performing optimization solution on a preset topological optimization model to obtain a unit density distribution map of the precision alignment platform;
And the alignment platform model drawing module is used for drawing boundary lines of the precision alignment platform unit density distribution diagram according to a preset unit density permission threshold value to obtain a precision alignment platform processing model surrounded by the boundary lines.
7. The apparatus of claim 6, wherein the design requirements further include requiring the parallel prototype mechanism to be a moving pair as an active pair.
8. The apparatus of claim 6, wherein the preset practical optimization goal is to maximize the working space of the parallel mechanism or maximize the load of the parallel mechanism.
9. The apparatus of claim 6, wherein the preset topology optimization model is constructed by a method comprising:
and taking the kinematic characteristics of the mechanism as an optimization design target, taking the difference value between the optimal input and output mapping matrix and the expected mapping matrix as an optimization constraint, and establishing the topological optimization model by adopting an SIMP method in a topological optimization method.
10. The apparatus of claim 6, wherein the preset topology optimization model is:
find x＝(x,x,...,x)
max f
V/V≤f
F＝KU
J·U＝U
E＝J-J≤m
wherein xe is a unit density, n is a total number of units in a design domain, Er is a difference value between an input/output mapping matrix and a given expected mapping matrix in a design process, fHz is a low-order modal frequency of the compliant mechanism, Ee is a young modulus of a unit E, Emin and E0 are unit young moduli when the unit densities are 0 and 1 respectively, p is a penalty factor, V is a compliant mechanism permitted volume, V0 is a compliant mechanism initial design area volume, fv is a volume fraction, F is an external force borne by the mechanism, K is a mechanism global stiffness, U is a mechanism global displacement, J is an input/output mapping matrix, Uin and Uout are displacements of a mechanism driving end and an output point respectively, x direction represents a driving freedom direction, y direction represents a direction perpendicular to x, λ is a ratio of two stiffness of an input end, and J is an expected mapping matrix, m is the allowable error between the actual mapping matrix and the expected mapping matrix.
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