Library search method for OCD measurement matching

Abstract

The present invention discloses a library search method for OCD measurement matching, including: experimentally measuring the experimental characteristic spectral data of a target structure; determining the range value and search accuracy value of a parameter group of the target structure; establishing a first database and a second database, where the first database contains a plurality of first simulated characteristic spectral data simulated according to the range value of the parameter group, and the second database is an empty database; initializing a search mode, a search position, and a search speed to generate a batch of particle swarms from the first database; initializing the individual extreme value and the global extreme value of the particle swarm; obtaining the matching error of all particles based on the search mode and the experimental characteristic spectral data; obtaining the current individual extreme value based on the matching error and updating the global extreme value; when the search termination condition is satisfied, obtaining the individual optimal solution based on the corresponding global extreme value to obtain the parameters of the corresponding particle as the structural parameters of the target structure. The present invention avoids a large amount of data redundancy and improves the matching efficiency and accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical measurement, and particularly relates to a library search method for OCD measurement matching. Background Art

[0002] With the continuous development of integrated circuits, the continuously shrinking structural dimensions and increasing structural complexity pose new challenges to nanoscale measurement technologies. The optical critical dimension (OCD) measurement technology can non-destructively and quickly measure samples, measure the TE (TM) reflectivity under variable wavelengths (variable angles), and then use rigorous coupled wave analysis to analyze the data to obtain the optical characteristic data of the samples. And through methods such as library search and optimization algorithms, the experimental data and simulation data are matched to obtain the simulation data with the smallest error to determine the parameters of the samples.

[0003] The traditional library search method is to establish a simulation model according to the approximate range of sample parameters, but the accuracy of the library search depends on the accuracy of the change of the simulation model: if the change accuracy of the simulation model is small, the library search may not be able to obtain accurate parameters; if the change accuracy of the simulation model is large, it will consume a large amount of time and storage memory, and the matching time will also increase accordingly. Therefore, it is necessary to select a suitable optimization algorithm for the library search method. Summary of the Invention

[0004] The purpose of the present invention is to provide a library search method for OCD measurement matching for the deficiencies of the prior art. By establishing an initial database with relatively low accuracy for initial search to determine the search direction, when it is judged that a search interval with higher accuracy is required, a second database with higher accuracy is generated by accessing the simulation software, which not only achieves the effect of high-precision matching, but also avoids the redundancy of a large amount of data and improves the matching efficiency.

[0005] To solve the above technical problems, the present invention adopts the following technical solutions:

[0006] A library search method for OCD measurement matching, which obtains the structural parameters of the target structure of the micro-nano structure based on the particle swarm algorithm, and the method includes the following steps:

[0007] Step S1, experimentally measure the target structure to obtain the experimental characteristic spectral data of the target structure;

[0008] Step S2, determine the range value and search accuracy value of the parameter group of the target structure according to the experimental characteristic spectral data;

[0009] Step S3: Establish a first database and a second database. The first database contains a plurality of first simulated characteristic spectral data simulated and generated according to the range values of the parameter group, and the second database is an empty database;

[0010] Step S4: Set the initial values of the search mode, search position, and search speed, and further generate a particle swarm composed of a preset number of particles based on the first database; and set the initial values of the individual extreme value and the global extreme value of the particle swarm;

[0011] Step S5: Obtain the matching errors corresponding to the preset number of particles based on the search mode and the experimental characteristic spectral data;

[0012] Step S6: Obtain the current individual extreme value based on all the matching errors, and update the global extreme value according to the current individual extreme value and the previous individual extreme value;

[0013] Step S7: When the search termination condition is satisfied, obtain the individual optimal solution based on the corresponding global extreme value, and further obtain the parameters of the corresponding particle as the structural parameters of the target structure.

[0014] Preferably, the step S5 includes:

[0015] Step S51: Obtain the search mode corresponding to each particle, and further obtain the particle according to the search position corresponding to the particle from the first database or the second database;

[0016] Step S52: Calculate the matching error between the first simulated characteristic spectral data corresponding to the obtained particle or the second simulated spectral data in the second database according to the experimental characteristic spectral data.

[0017] Preferably, in the step S51, setting the search mode includes the following three types: obtaining the particle from the first database, obtaining the particle from the second database, and setting the matching error of the current particle to negative infinity;

[0018] The step 51 includes:

[0019] Step S511: When the search mode is to obtain the particle from the first database, judge whether there is a corresponding particle in the first database based on the search position. If not, obtain the particle closest to the search position;

[0020] Step S512: When the search mode is to obtain the particles from the second database, determine whether there are corresponding particles in the second database based on the search position. If not, call the simulation software and generate the matching second simulation spectral data in the second database according to the search position.

[0021] Preferably, in step S52, if the number of particles selected in step S5 is set to m, the matching error corresponding to the m particles is expressed as S = [S1, S2, S3......S m , and the matching error is obtained by the following formula:

[0022]

[0023] In the formula, n is the number of discrete points of the characteristic spectral data, R(r i ) is the i-th value of the experimental spectral data, and R m ′(r i ′) is the i-th value of the first simulation spectral data or the second simulation spectral data corresponding to the m-th group of parameter values.

[0024] Preferably, before step S7, it further includes:

[0025] Step S7a: Determine whether the search termination condition is satisfied. If so, execute step S7; if not, execute the following steps:

[0026] Step S7b: Update the search speed based on a preset rule;

[0027] Step S7c: Update the search mode and the search position according to the search speed to update the particle swarm; and return to step S5.

[0028] Preferably, in step S7a, the search termination condition at least includes the following conditions: whether the loop composed of step S5, step S6, step S7b, and step S7c meets the preset loop count requirement; or, whether the matching error obtained in step S6 meets the preset accuracy requirement.

[0029] Preferably, in step S7b, the preset rule is:

[0030] If the number of particles selected in step S5 is set to m, the corresponding search position is expressed as X = [x1, x2,......x m and the corresponding search speed is expressed as V = [v1, v2,......v m , and in the process of obtaining the individual extreme value and the global extreme value, each group of particles updates the search speed through the following formula:

[0031] v = v + c1 × rand × (pBest - present) + c2 × rand × (gBest - present)

[0032] Wherein, present is the position of the current particle, pBest is the individual extreme value, gBest is the global extreme value, rand is a random number between 0 and 1, and c1 and c2 are learning factors.

[0033] Preferably, in the step S7c, each group of particles updates the search position based on the following formula according to the search speed:

[0034] present = present + v

[0035] Wherein, present is the position of the current particle, and v is the search speed of the particle.

[0036] Preferably, in the step S7c, the search speed v is limited within the set maximum speed v max If the updated v exceeds v max , then the current search speed is v max ;

[0037] Set v limit1 and v limit2 , where v limit1 << v limit2 , initialize the counters Counter1 and Counter2 to 0, and set their upper limits to C1 and C2;

[0038] The process of updating the search pattern according to the search speed includes:

[0039] Step S7c1, obtain the search speed v corresponding to the current particle;

[0040] Step S7c2, judge v and v limit1 , if v < v limit1 , then Counter1 increments by 1; otherwise, directly execute step S7c4;

[0041] Step S7c3, judge v and v limit2 , if v < v limit2 , then Counter2 increments by 1; otherwise, directly execute step S7c4;

[0042] Step S7c4, judge whether Counter1 is greater than C1. If so, set the matching error of the corresponding current particle to negative infinity; if not, execute step S7c5;

[0043] Step S7c5: Determine whether Counter2 is greater than C2. If so, set the corresponding search pattern to obtain the particle from the first database; otherwise, set the corresponding search pattern to obtain the particle from the second database.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows: The library search method of the present invention estimates the range value of the parameter group of the target structure based on the experimental measurement of the test characteristic spectrum data of the target structure, and preset the search accuracy. Further, a large number of simulated characteristic spectrum data are generated by simulation according to the estimated range of the parameter group and stored in the established first database. At the same time, an empty second database is established. After initializing the search pattern, search position and search speed, a group of particle swarms are initialized according to the first database, and the individual extreme value and global extreme value of the particle swarm are initialized. Further, according to the search pattern and the experimental characteristic spectrum data, the matching error of each particle in the particle swarm is calculated, and the individual extreme value of the current particle swarm is obtained based on all the calculated matching errors, so as to update the global extreme value of the particle swarm. When the preset search termination condition is met, the individual optimal solution is obtained according to the current global extreme value, so as to obtain the parameters of the corresponding particle as the structural parameters of the target structure. The present invention uses the first database with lower precision (larger step size) for preliminary search to determine an effective approximate search direction. When the matching error of the simulation data reaches the set threshold, the simulation software is called to generate a second database with higher precision, and the search is carried out in the second database. This method can flexibly change the precision of the database, reduce the operation cost of the high-precision database, and achieve the effect of short-time and high-efficiency matching of structural parameters. Description of the Drawings

[0045] Figure 1 is the flowchart of the library search method for OCD measurement matching in the embodiment of the present invention.

[0046] Figure 2 is the flowchart of the matching error calculation process of the particle swarm in the embodiment of the present invention.

[0047] Figure 3 is the flowchart of the search pattern update process in the embodiment of the present invention. Detailed Embodiment

[0048] The present invention will be further described below with reference to the embodiments shown in the drawings.

[0049] As shown in the Figures 1 to 3 accompanying drawings, this embodiment discloses a library search method for OCD measurement matching, which obtains the structural parameters of the target structure of the micro-nano structure through a particle swarm algorithm. The method includes the following steps:

[0050] Step S1: Conduct an experiment to measure the target structure to obtain the experimental characteristic spectral data R = [r1, r2,......r n , where a set of spectral data contains n discrete points.

[0051] Step S2: Determine the range value and search accuracy value of the parameter group of the target structure according to the experimental characteristic spectral data. For example, if the target structure is a one-dimensional grating structure, its parameter group can be P = [TopCD, LowCD, Pitch, Height, SWA].

[0052] Step S3: Establish a first database and a second database. The first database contains multiple first simulation characteristic spectral data R′ = [r1′, r2′,......r n ′] generated by simulation according to the range value of the parameter group. Among them, there is a one-to-one mapping relationship between the spectral data and the particle positions. The parameter space range defined by the first database is large, the accuracy is low, the step size of parameter change is large, and the data volume is small, which is convenient for rough preliminary search. The second database is an empty database.

[0053] Step S4: Set the initial values of the search mode flag, search position, and search speed, and further generate a particle swarm composed of a preset number of particles based on the first database; and set the initial values of the individual extreme value and global extreme value of the particle swarm.

[0054] Step S5: Obtain the matching error corresponding to the preset number of particles based on the search mode and the experimental characteristic spectral data.

[0055] Specifically, Step S5 includes:

[0056] Step S51: Obtain the search mode corresponding to each particle, and further obtain the particle according to the search position corresponding to the particle from the first database or the second database.

[0057] In Step S51, setting the search mode includes the following three situations: obtaining particles from the first database (the corresponding flag value is defined as 1), obtaining particles from the second database (the corresponding flag value is defined as 0), and setting the matching error of the current particle to negative infinity (the corresponding flag value is defined as 2). It should be noted here that in Step S4, the initial value of the search mode flag is set to 1, so that a batch of particle swarms can be initialized from the first database.

[0058] Furthermore, the specific process of Step 51 includes:

[0059] Step S511: When the search mode is to obtain particles from the first database, i.e., flag = 1, it is determined whether there are corresponding particles in the first database based on the search position. If not, the particle closest to the search position is obtained.

[0060] Step S512: When the search mode is to obtain particles from the second database, i.e., flag = 0, it is determined whether there are corresponding particles in the second database based on the search position. If not, the simulation software is called and the matching second simulation spectral data is generated in the second database according to the search position.

[0061] Then, step S52 is executed: The matching error is calculated for the first simulation characteristic spectral data corresponding to the obtained particles or the second simulation spectral data in the second database according to the experimental characteristic spectral data.

[0062] Specifically, in step S52, it is assumed that the number of particles selected in step S5 is m. Then the matching error corresponding to the m particles is expressed as S = [S1, S2, S3......S m , and the matching error is obtained by the following formula:

[0063]

[0064] In the formula, n is the number of discrete points of the characteristic spectral data, R(r i ) is the i-th value of the experimental spectral data, and R m ′(r i ′) is the i-th value of the first simulation spectral data or the second simulation spectral data corresponding to the m-th group of parameter values.

[0065] Step S6: Based on all the matching errors, the current individual extreme value is obtained, and the global extreme value is updated according to the current individual extreme value and the previous individual extreme value.

[0066] Step S7: When the search termination condition is satisfied, the individual optimal solution is obtained based on the corresponding global extreme value, and the parameters of the corresponding particle are further obtained as the structural parameters of the target structure.

[0067] In another embodiment, before step S7, it further includes:

[0068] Step S7a: It is determined whether the search termination condition is satisfied. If so, step S7 is executed; if not, step S7b and step S7c are executed.

[0069] Specifically, in step S7a, the search termination condition at least includes the following conditions: Whether the loop composed of step S5, step S6, step S7b, and step S7c meets the preset loop count requirement; or, whether the matching error obtained in step S6 meets the preset accuracy requirement.

[0070] Step S7b: Update the search speed based on a preset rule. The preset rule is as follows:

[0071] Set the number of particles selected in Step S5 as m, and set the corresponding search positions as X = [x1, x2,... x m and the corresponding search speeds as V = [v1, v2,... v m . During the process of obtaining the individual extreme value and the global extreme value, each group of particles updates the search speed through the following formula:

[0072] v = v + c1 × rand × (pBest - present) + c2 × rand × (gBest - present)

[0073] In the formula, present is the position of the current particle, pBest is the individual extreme value, gBest is the global extreme value, rand is a random number between 0 and 1, and c1 and c2 are learning factors.

[0074] Step S7c: Update the search pattern and search position according to the search speed to update the particle swarm; and return to Step S5.

[0075] Specifically, in Step S7c, each group of particles updates the search position based on the following formula according to the search speed:

[0076] present = present + v

[0077] In the formula, present is the position of the current particle, and v is the search speed of the particle.

[0078] In addition, in Step S7c, the search speed v is restricted within the set maximum speed v max . If the updated v exceeds v max , then the current search speed is v max .

[0079] Set v limit1 and v limit2 , where v limit1 << v limit2 , that is, v limit1 is much smaller than v limit2 . Initialize the counters Counter1 and Counter2 to 0, and set their upper limits as C1 and C2. In a specific embodiment, C1 = C2 can be set.

[0080] Then, the process of updating the search pattern according to the search speed includes:

[0081] Step S7c1: Obtain the search speed v corresponding to the current particle.

[0082] Step S7c2: Judge v and v limit1 If v < v limit1 , then Counter1 increments by 1; otherwise, directly execute Step S7c4.

[0083] Step S7c3: Judge v and v limit2 If v < v limit2 , then Counter2 increments by 1; otherwise, directly execute Step S7c4.

[0084] Step S7c4: Judge whether Counter1 is greater than C1. If so, it indicates that the particle search speed v in this dimension is always too slow, and the particle position path range is less than the limited precision. Then, the particle will not be updated subsequently. Correspondingly, set the corresponding search mode to set the matching error of the current particle to negative infinity, that is, update flag = 2. If not, then execute Step S7c5.

[0085] Step S7c5: Judge whether Counter2 is greater than C2. If so, set the corresponding search mode to obtain particles from the first database. If not, it indicates that the particle in this dimension always maintains an appropriate speed, and the particle position path range is close to the optimal parameter group, and a more accurate search can be carried out in the next step. Correspondingly, set the corresponding search mode to obtain particles from the second database, that is, update flag = 0.

[0086] The library search method of this embodiment estimates the range value of the parameter group of the target structure based on the experimental characteristic spectral data of the target structure measured experimentally, and preset the search accuracy. Further, a large number of simulated characteristic spectral data are generated by simulation according to the estimated parameter group range and stored in the established first database. At the same time, an empty second database is established. After initializing the search mode, search position, and search speed, a batch of particle swarms are initialized according to the first database, and the individual extreme value and global extreme value of the particle swarm are initialized. Further, calculate the matching error of each particle in the particle swarm according to the search mode and experimental characteristic spectral data, and obtain the individual extreme value of the current particle swarm based on all the calculated matching errors, so as to update the global extreme value of the particle swarm. When the preset search termination condition is met, obtain the individual optimal solution according to the current global extreme value, so as to obtain the parameters of the corresponding particle as the structural parameters of the target structure.

[0087] This method is based on library search for matching. By judging the error magnitude between experimental data and simulation data, it determines whether the simulation data is close to the true value. Specifically, it first performs a preliminary search using a first database with lower precision (larger step size) to determine an effective approximate search direction. When the matching error of the simulation data reaches the set threshold, it then calls the simulation software to generate a second database with higher precision and conducts a search in the second database. Finally, a set of simulation data with the smallest matching error is obtained, and the model parameters corresponding to this simulation data are the structural parameters (i.e., profile parameters) of the target structure. This method can flexibly vary the precision of the database, reduce the computational cost of the high-precision database, and achieve the effect of short-time and high-efficiency matching of structural parameters.

[0088] The library search method of this embodiment initializes a group of random particles (random solutions). All particles have a corresponding matching error. The smaller the matching error, the better the corresponding particle. The optimal solution is found through iteration. In each iteration, the particle updates itself by tracking two extreme values. The first is the optimal solution found by the particle itself, which is called the personal best pBest. The other extreme value is the optimal solution found by the entire population, which is the global best gBest. Eventually, the optimal solution that meets the precision requirements is found. These two extreme values are updated to the corresponding optimal solutions in each round of iteration.

[0089] The protection scope of the present invention is not limited to the above embodiments. Obviously, those skilled in the art can make various changes and deformations to the present invention without departing from the scope and spirit of the present invention. If these changes and deformations fall within the scope of the claims of the present invention and their equivalent technologies, the intention of the present invention also includes these changes and deformations.

Claims

1. A library search method for OCD measurement matching, which obtains the structural parameters of the target structure of the micro-nano structure based on the particle swarm algorithm, is characterized in that, The method includes the following steps: Step S1: Experimentally measure the target structure to obtain the experimental characteristic spectral data of the target structure; Step S2: Determine the range value and search accuracy value of the parameter group of the target structure according to the experimental characteristic spectral data; Step S3: Establish a first database and a second database. The first database contains a plurality of first simulation characteristic spectral data generated by simulation according to the range value of the parameter group, and the second database is an empty database; Step S4: Set the initial values of the search mode, search position, and search speed. Further generate a particle swarm composed of a preset number of particles based on the first database; and set the initial values of the individual extreme value and global extreme value of the particle swarm; Step S5: Obtain the matching error corresponding to the preset number of particles based on the search mode and the experimental characteristic spectral data; including: Step S51: Obtain the search mode corresponding to each particle, and further obtain the particle according to the search position corresponding to the particle from the first database or the second database; Step S52: Calculate the matching error between the first simulation characteristic spectral data corresponding to the obtained particle or the second simulation spectral data in the second database according to the experimental characteristic spectral data; In step S51, it is set that the search mode includes the following three types: obtaining the particle from the first database, obtaining the particle from the second database, and setting the matching error of the current particle to negative infinity; Step S51 includes: Step S511: When the search mode is to obtain the particle from the first database, judge whether there is a corresponding particle in the first database based on the search position. If not, obtain the particle closest to the search position; Step S512: When the search mode is to obtain the particle from the second database, judge whether there is a corresponding particle in the second database based on the search position. If not, call the simulation software and generate the matching second simulation spectral data in the second database according to the search position; Step S6: Obtain the current individual extreme value based on all the matching errors, and update the global extreme value according to the current individual extreme value and the previous individual extreme value; Step S7: When the search termination condition is met, obtain the individual optimal solution based on the corresponding global extreme value, and further obtain the parameters of the corresponding particle as the structural parameters of the target structure.

2. The library search method for OCD measurement matching according to claim 1, wherein: In the step S52, if the number of particles selected in the step S5 is set to be m, the matching errors corresponding to the m particles are expressed as , and the matching errors are obtained by the following formula: where n is the number of discrete points of the characteristic spectral data, is the i -th value of the experimental spectral data, is the i -th value of the first simulated spectral data or the second simulated spectral data corresponding to the m-th set of parameter values.

3. The library search method for OCD measurement matching according to claim 1, wherein: Before step S7, it further includes: Step S7a: Judge whether the search termination condition is met. If so, execute step S7; if not, execute the following steps: Step S7b: Update the search speed based on a preset rule; Step S7c: Update the search mode and the search position according to the search speed to update the particle swarm; and return to step S5.

4. The library search method for OCD measurement matching according to claim 3, wherein: In the step S7a, the search termination condition at least includes the following conditions: whether the loop composed of the step S5, the step S6, the step S7b, and the step S7c meets the preset loop number requirement; or, whether the matching error obtained in the step S6 meets the preset accuracy requirement.

5. The library search method for OCD measurement matching according to claim 3, wherein: In the step S7b, the preset rule is: Set the number of particles selected in the step S5 as m, and set the corresponding search position as and the corresponding search velocity as . In the process of obtaining the individual extreme value and the global extreme value, each group of particles updates the search velocity through the following formula: where present is the position of the current particle, pBest is the individual extreme value, gBest is the global extreme value, rand is a random number between 0 and 1, and c1 and c2 are learning factors.

6. The library search method for OCD measurement matching according to claim 5, wherein: In the step S7c, according to the search speed, each group of particles updates the search position based on the following formula: where present is the position of the current particle, is the search velocity of the particle.

7. The library search method for OCD measurement matching according to claim 6, wherein: In the step S7c, the search speed is limited to a set maximum speed within, if the updated exceeds, then the current search speed is ; Set and wherein initialize counter and to 0, and set its upper limit to and ; The process of updating the search mode according to the search speed includes: Step S7c1, obtain the search velocity corresponding to the current particle ; Step S7c2, check and and if , then increment by 1; otherwise, directly execute Step S7c4; Step S7c3, check with and if , then increment by 1; otherwise, directly execute Step S7c4; Step S7c4, determine whether it is greater than , if so, set the corresponding search pattern to set the matching error of the current particle to negative infinity; if not, execute step S7c5; Step S7c5, determine whether it is greater than , if so, set the corresponding search pattern to obtain the particle from the first database; if not, set the corresponding search pattern to obtain the particle from the second database.

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