Method for calculating photoresist state change time in PEB in real time

Abstract

The invention provides a method for calculating photoresist state change time in PEB in real time. Comprising the following steps: a preposition step: uniformly or non-uniformly dividing a three-dimensional data structure of photoresist film information data which at least comprises spatial position information into a lattice tendency function and a state tendency function of a plurality of cells to confirm an overall tendency function of the three-dimensional data structure; circulating the steps L1-L2, wherein the step L1: in the process of simulating the PEB, sequentially confirming a cell, a reaction type and / or diffusion with state change by introducing an overall tendency function, a lattice tendency function and a state tendency function of a simulation random number r; forming a simulation result or triggering a boundary condition to form the simulation result; updating and forming an overall tendency function, a lattice tendency function and a state tendency function according to a simulation result; wherein 0 lt; rlt; 1; and step L2, calculating the time taum of the next state change by using a formula (1). The method has the beneficial technical effects that the random reaction diffusion phenomenon in the PEB process can be simulated at high precision from the molecular level and can be output in real time.

Description

Technical Field

[0001] The present invention belongs to the field of semiconductor integrated circuit manufacturing, and particularly relates to a method for real-time calculating the time of change in the state of photoresist in PEB. Background Art

[0002] Lithography technology is widely used in the manufacture of semiconductor integrated circuits. In the manufacturing process, after exposure, the wafer needs to be immediately transferred to a hot plate in a spin coater-developer for baking, that is, post-exposure bake (PEB), and PEB is one of the most important steps in the lithography process. Chemically amplified resist (CAR) can significantly improve the quantum efficiency of photoresist. It mainly includes polymer resin, photoacid generator (PAG), etc. PAG is a photosensitive compound that decomposes under light to generate photoacid (H+). In the PEB step, the photoacid plays a catalytic role, which can cause the side chains of the polymer resin to undergo a deprotection reaction by the protecting group, generating soluble hydroxyl groups (-OH). The shedding of the protecting group changes the polarity of the polymer resin. As the number of deprotected groups gradually increases, the photoresist can dissolve in the developer and show the morphology in the subsequent development step.

[0003] US Patent US6295637B1 discloses a method for simulating the state of CAR with photoacid and protecting groups in the PEB process. The solution simulates the post-exposure bake (PEB) process of a chemically amplified resist with photoacid and protection sites, uses the initial PEB parameters to represent the temperature-time history of the PEB process, and uses the reaction constants related to temperature and the diffusion coefficients related to temperature and protection sites during the entire PEB simulation to represent the chemically amplified resist. It adopts implicit calculation of the concentration of the protected part and the concentration of photoacid of the chemically amplified resist, and uses implicit calculation according to the diffusion coefficient in the space occupied by the chemically amplified resist, so as to simulate the state and properties of the photoresist. The calculation complexity of this solution is high and it cannot output the state of each part of the photoresist in real time.

[0004] With the continuous iteration of technology nodes, the minimum line width of lithography technology has been less than 10 nanometers. At such a small line width scale, calculating the spatial distribution of the side chain groups of the polymer resin inside the photoresist and considering the results of the random reaction diffusion of photoacid at the molecular level are crucial for controlling the line edge roughness (LER). Summary of the Invention

[0005] In view of the scenario where the calculation steps of the reaction-diffusion model inside the photoresist in the prior art are lengthy, the randomness of reaction-diffusion cannot be considered, and the real-time performance is poor, the present invention provides a method for calculating the time of state change of the photoresist in PEB in real time.

[0006] A method for calculating the time of state change of the photoresist in PEB in real time, comprising:

[0007] Pre-step: Confirm the overall tendency function of the three-dimensional data structure with a grid tendency function that evenly or unevenly divides the three-dimensional data structure of the photoresist film information data configured to at least include spatial position information into several cells and a state tendency function of the state change of the cells; the spatial position information at least includes the spatial position information of the side chain groups on the upper side of the resin polymer chain in the photoresist, the distribution positions of photoacid and base neutralizer; the state change types include reaction type and diffusion;

[0008] Loop steps L1 to L2,

[0009] Step L1: Simulate the overall tendency function, grid tendency function, and state tendency function that introduce the simulation random number r during the PEB process to sequentially confirm the cells where state changes occur, reaction types, and / or diffusion; form a simulation result or trigger a boundary condition to form a simulation result; update and form the overall tendency function, grid tendency function, and state tendency function according to the simulation result; wherein, 0 < r < 1;

[0010] Step L2: Calculate the time τ of the next state change using formula (1) m :

[0011]

[0012] wherein, m is the serial number of the next state change; R m is the timing random number of the next state change, with a value of 0 < R m < 1; a i is the grid tendency function updated and formed in step L1, N is the number of cells, and i takes values of 1 ≤ i ≤ N, is the overall tendency function updated and formed in step L1.

[0013] Preferably, before the loop step, it also includes calculating the time τ1 of the first state change using formula (2):

[0014]

[0015] R1 is the random number of the first state change, with a value of 0 < R1 < 1; a i is the grid tendency function in the pre-step, N is the number of cells, and i takes values of 1 ≤ i ≤ N, is the overall tendency function in the pre-step.

[0016] Preferably, the types and sorting of the state tendency functions of each cell are the same.

[0017] Preferably, the control time limit is 30 seconds to 180 seconds.

[0018] Preferably, the boundary conditions include reflective boundary conditions or periodic boundary conditions.

[0019] Preferably, in step L1,

[0020] i starts the operation of formula (3) from the minimum value of 1 to confirm the cells where state changes occur.

[0021] selector1 = a0 * r,

[0022] selector i+1 = selector i - a i , i = 1,... N (3)

[0023] When selector i+1 ≤ 0, stop and confirm that the state of the i-th cell will change; where a0 is the overall tendency function in the previous step or the overall tendency function updated in L1, and a i is the cell tendency function of the i-th cell in the previous step or the cell tendency function of the i-th cell updated in L1, and N is the number of cells.

[0024] j starts the operation of formula (4) from the maximum value of M to confirm the type of state change in the i-th cell.

[0025] selector i,M = selector i+1 ;

[0026] selector i,j-1 = selector i,j + b j , j = M,... 1 (4)

[0027] When selector i,j-1 > 0, stop and confirm the state change corresponding to the state tendency function b j in the i-th cell; where b j is the state tendency function of the i-th cell in the previous step or the state tendency function updated in step L1; M is the sum of the total number of reaction types and the number of diffusion substances in the three-dimensional data structure.

[0028] If b jThe correspondence is a reaction, and subtracting a reaction update forms b j And / or other state changes affected by the reaction within the i-th cell are updated to form a state tendency function, and the lattice tendency function of the i-th cell and the overall tendency function are updated with it, and step L2 is executed with it;

[0029] If b j The correspondence is diffusion, and k starts operating formula (5) from the minimum value of 1 to confirm the diffusion direction of the i-th cell:

[0030] selector i,j-1,1 = selector i,j-1

[0031] selector i,j-1,k+1 = selector i,j-1,k -c k , k = 1, … p (5)

[0032] When selector i,j-1,k+1 ≤ 0, stop, and confirm the diffusion function c k Diffuse the corresponding diffusing substance to the target cell in the corresponding diffusion direction; update the state tendency function of this diffusion of the i-th cell and the target cell and / or update the state tendency function of other state changes affected by the diffusing substance within the i-th cell and the target cell, and update the lattice tendency function of the i-th cell and the target cell and the overall tendency function with it, and execute step L2 with it. k Preferably, all cells are hexahedrons and the p value is 6; alternatively, the cells are tetrahedrons or octahedrons, and the corresponding p values are 4 or 8.

[0033] Preferably, the reaction includes group deprotection or acid-base neutralization or acid loss.

[0034] Preferably, the reaction includes group deprotection or acid-base neutralization or acid loss.

[0035] The method for real-time calculating the time of the state change of the photoresist in PEB of the present invention can simulate the random reaction diffusion phenomenon in the PEB process at the molecular level with high precision and output the side chain group state in real time. By adopting a simple loop of "positive subtraction - negative addition - positive subtraction" traversal, the calculation complexity is greatly reduced, and the PEB working hours can be quickly simulated and calculated and output. It has strong real-time performance and is more conducive to the processing of high-precision integrated circuits. Brief Description of the Drawings

[0036] The following will further illustrate the above characteristics, technical features, advantages and their implementation manners in a clear and easy-to-understand manner in combination with the drawings in the preferred embodiments.

[0037] Figure 1 Flowchart of the method for real-time calculating the time of the state change of the photoresist in PEB of the present invention;

[0038] Figure 2 For Figure 1 The flowchart for updating the overall tendency function in step L1

[0039] Figure 3 The structural schematic diagram of the three-dimensional data structure of the photoresist of the present invention

[0040] Figures 4A to 4B It is a schematic diagram for updating the diffusion tendency function, state tendency function, lattice tendency function, and overall tendency function when diffusion substances diffuse within the unit cell of the present invention

[0041] Figures 5A to 5C It is a schematic diagram for updating the state tendency function, lattice tendency function, and overall tendency function when a reaction occurs within the unit cell of the present invention

[0042] Figure 6 It is a schematic diagram of the information exchange storage strategy based on reactions of the present invention Detailed implementation manners

[0043] The following further details each aspect of the present invention

[0044] Unless otherwise defined or described, all professional and scientific terms used herein have the same meaning as those familiar to persons skilled in the art. In addition, any methods and materials similar or equivalent to the described content can be applied to the present invention

[0045] The following explains the terms

[0046] Unless otherwise clearly specified and limited, the "or" described in the present invention includes the relationship of "and". The "and" is equivalent to the Boolean logic operator "AND", the "or" is equivalent to the Boolean logic operator "OR", and "AND" is a subset of "OR"

[0047] It can be understood that although terms such as "first", "second", etc. can be used herein to describe different elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. Therefore, a first element can be called a second element without departing from the teachings of the concept of the present invention

[0048] In the present invention, the terms "contain", "include" or "comprise" mean that various components can be applied together to the mixtures or compositions of the present invention. Therefore, the term "consisting essentially of..." is included in the terms "contain", "include" or "comprise"

[0049] Unless otherwise clearly defined and limited, the terms "connected", "communicated with", and "coupled" in the present invention should be understood in a broad sense. For example, it may be a fixed connection, or may be connected through an intermediate medium, or may be the communication inside two components or the interaction relationship between two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to specific situations.

[0050] For example, if one element (or component) is said to be on another element, coupled with or connected to another element, then the one element may be directly formed on, coupled with or connected to the other element, or there may be one or more intermediate elements between them. On the contrary, if the expressions "directly on...", "directly coupled with..." and "directly connected with..." are used herein, it means that there are no intermediate elements. Other words used to describe the relationship between elements should be interpreted similarly, such as "between..." and "directly between...", "attached" and "directly attached", "adjacent" and "directly adjacent", etc.

[0051] In addition, it should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to the directions in the drawings. The words "inner" and "outer" respectively refer to the directions towards or away from the geometric center of a specific component. It can be understood that here, these terms are used to describe the relationship of one element, layer or region relative to another element, layer or region as shown in the drawings. Except for the orientations described in the drawings, these terms should also cover other orientations of the device.

[0052] Other aspects of the present invention will be obvious to those skilled in the art due to the disclosure herein.

[0053] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the specific embodiments of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to these drawings, and other embodiments can also be obtained.

[0054] It should also be noted that the illustrations provided in the following embodiments only schematically illustrate the basic concept of the present application. The drawings only show the components related to the present application, rather than being drawn according to the number, shape and size of the components in actual implementation. The types, numbers and proportions of the components in actual implementation can be arbitrarily changed, and the component layout type may also be more complex. For example, the thickness of the elements in the drawings may be exaggerated for clarity.

[0055] As shown Figures 1 to 6 in the figure, the present invention provides a method for calculating the time of change in the state of photoresist in PEB in real time, including

[0056] Pre-step 100: Confirm the overall tendency function of the three-dimensional data structure with a grid tendency function that evenly or unevenly divides the three-dimensional data structure of photoresist film information data configured to at least include spatial position information into several cells and a state tendency function of the state change of the cells; the spatial position information at least includes the spatial position information of the side chain groups on the resin polymer chains in the photoresist, the distribution positions of photoacids and base neutralizers in the photoresist film, the deprotection reaction rate constants of different types of protected groups in the photoresist film, the acid diffusion coefficient in the photoresist film, the base diffusion coefficient in the photoresist film, the acid loss rate constant in the photoresist film, and / or the acid-base neutralization rate constant in the photoresist film; introducing molecular structure information can predict and simulate the state change of photoresist in PEB from the molecular level.

[0057] In this embodiment, as shown Figure 3 in the figure, the three-dimensional data structure 1 of the photoresist film information data is evenly divided into cells 11, 12, 13, 14... 1N (not shown) in the shape of a cuboid or cube. This kind of division is conducive to simplifying the processing. In other embodiments, the three-dimensional data structure 1 can be unevenly divided according to the spatial position information, especially the spatial position information of groups (such as various groups participating in the reaction) and the distribution positions of diffusing substances (such as photoacids and base neutralizers). In another division embodiment (not shown), the inventor takes as the benchmark that the distribution of groups and diffusing substances in each cell conforms to a certain rule (such as uniform distribution), so that the reaction / diffusion in each cell is uniform. The divided cells include tetrahedrons, hexahedrons, octahedrons, etc. It should be noted that the overall tendency function of a certain amount of photoresist (assuming the whole is set as a three-dimensional data structure) at the initial moment of PEB is determined by the spatial position information it contains. Because the internal spatial position information formed by the photoresist is different under different processes or conditions, the amount of spatial position information in the divided cells will directly determine the state tendency function and grid tendency function of the cell. During the PEB process, as the chemical reaction, especially the deprotection reaction, proceeds, the overall tendency function tends to decrease.

[0058] By forming a three-dimensional data structure corresponding to the shape of the photoresist film according to the information data of the photoresist film with spatial position information, this three-dimensional data structure can be regarded as a set of points in a three-dimensional coordinate system. The information data of a photoresist film with spatial position information can be derived from the results of coarse-grained molecular dynamics.

[0059] The three-dimensional data structure can be segmented. In the form of segmenting a photoresist film, the three-dimensional data structure can be segmented into a plurality of cells, such that each cell corresponds to the position of a three-dimensional region on the photoresist. Each cell contains the groups, the amounts of photoacid and base, and the corresponding data information in the corresponding region of the photoresist. On this basis, the cells can be divided in the form of multi-layer stacking. The specific shape of each cell is preferably a hexahedron, such as a cube or a cuboid. The hexahedron shape is first convenient for combining into the three-dimensional shape of the photoresist film, and at the same time is also convenient for subsequent calculation of the diffusion direction of the cells. On this basis, the state tendency function of various state changes in each cell, the cell tendency function of each cell, and the overall tendency function of the corresponding three-dimensional data structure can be calculated through the above information data. A three-dimensional number is assigned to each cell according to its position in the three-dimensional data structure, and the three-dimensional number is made one-dimensional. There are many ways to make the three-dimensional number one-dimensional. For example, the three-dimensional number (x, y, z) can be converted into a one-dimensional number (x * y * z), which is convenient for subsequent traversal calculation. It should be noted that this embodiment is only an example for illustrating the feasibility of the technical solution and cannot limit the protection scope of the present invention.

[0060] In the pre-step 100 of this embodiment and the one-cycle step 200 hereinafter, the overall tendency function is the sum of the cell tendency functions of all cells, and the cell tendency function is the sum of the state tendency functions of all states of the cell. In the pre-step 100 and the one-cycle step 200 of other embodiments, the overall tendency function can be the linear or non-linear simulation sum of the cell tendency functions of all cells, and the cell tendency function is the linear or non-linear simulation sum of the state tendency functions of all states of the cell. In the pre-step 100 and the one-cycle step 200 of another embodiment, the overall tendency function can also be the linear or non-linear simulation sum of the cell tendency functions of all cells in the middle part of the normal distribution. The adjustment of the overall tendency function is subject to the fitting with the actual process in the subsequent stage, and the applicant will not elaborate here.

[0061] As Figures 4A to 5C shown, the state change types include reaction type and diffusion; reaction refers to the chemical reaction of various substances inside the photoresist during the PEB process, and diffusion refers to the flow diffusion of the diffusing substances inside the photoresist. In this application, the M value is the sum of the types of reaction types and the types of diffusing substances. The reaction certainly also includes group deprotection, acid-base neutralization, or acid loss.

[0062] As Figures 4A to 5CAs shown, the sorting of the types (i.e., quantities) of state tendency functions for each cell is the same. That is, a single sorting is performed based on all chemical reaction types and all diffusion substance types in the three-dimensional data structure, and all cells use this sorting, which does not change during a complete PEB simulation process. It should be noted that since the state tendency function also includes the diffusion tendency function corresponding to diffusion, when the reaction change indicated by the state tendency function is diffusion, as described above, in this embodiment, the state tendency function is the sum of the diffusion tendency functions in all diffusion directions with a total quantity of p; in other embodiments, the state tendency function is the linear or non-linear simulation sum of the diffusion tendency functions in all diffusion directions with a total quantity of p; the diffusion tendency function includes direction information for pointing to the target cell to indicate its destination / direction of diffusion of the diffusion substance. The value of p is determined by the shape of the cell obtained when dividing the three-dimensional data structure as described above. For example, if the obtained cell is a tetrahedron, the state tendency function for the diffusion of one diffusion substance in this cell has 4 diffusion tendency functions with a p value of 4, and so on. The p value for a hexahedron is 6, and the p value for an octahedron is 8.

[0063] In this embodiment, the lattice tendency function a is calculated using formula (6) i ,

[0064]

[0065] where a i is the lattice tendency function of the i-th cell; b j is the j-th state tendency function of all state changes in the i-th cell.

[0066] In this embodiment, if the state change is a unimolecular reaction, b j = k j1 n1, k j1 is the reaction rate constant of the unimolecular reaction (unit 1 / s), and n1 is the number of the unimolecular reactant in this cell.

[0067] In this embodiment, if the state change is a bimolecular reaction, b j = k j2 n2n3 / dx / dy / dz, k j2 is the reaction rate constant of the bimolecular reaction (unit nm 3 / s), n2 and n3 are respectively the numbers of the bimolecular reactants in this cell, dx, dy, and dz are respectively the lengths of the cell in the x, y, and z directions, and dxdydz determines the value size of the lattice tendency function of different cells according to the cell position or size.

[0068] In this embodiment, if the state change is the diffusion of one diffusion substance, b jx = 2b x , b x = Dj n4 / dx / dx is the diffusion tendency function of the diffusing substance in the positive and negative x-directions, b jy = 2b y ,b y = D j n4 / dy / dy is the diffusion tendency function of the diffusing substance in the positive and negative y-directions, b jz = 2b z ,b z = D j n4 / dz / dz is the diffusion tendency function of the diffusing substance in the positive and negative z-directions, D j is the diffusion coefficient (unit nm 2 / s), n4 is the number of the diffusing substance in the cell; then the state tendency function b of the diffusion of the substance j = b jx + b jy + b jz .

[0069] In this embodiment, the overall tendency function a is calculated using formula (7) in the present pre-step 100 and subsequent loop step 200,

[0070]

[0071] where a is the overall tendency function of the three-dimensional data structure; a i is the cell tendency function of the i-th cell; N is the number of all cells in the three-dimensional data structure. That is, the overall tendency function of the entire three-dimensional data structure can be obtained by accumulating the cell tendency functions of each cell.

[0072] As a simple example, as Figure 3 shown, the state changes included in cell 13 are 3 reactions and 2 diffusions, a total of 5 state changes. Therefore, the M value corresponding to cell 13 is 5. Formula (6) obtains the cell tendency function of cell 13 by accumulating the state tendency functions of all state changes in the cell. Then Figure 3 as shown in cell 13 (corresponding to cell #3 in Figure 4A and Figure 5A in the pre-step 100), the initial cell tendency function value calculated in the pre-step 100 is 12.3.

[0073] Similarly, as Figure 3 shown, the second state change of the hexahedral cell 13 is diffusion one, which includes 6 diffusion tendency functions 132 in 6 directions. In this embodiment, the sum of the values of the 6 diffusion tendency functions 132 is the state tendency function 2 of diffusion one.

[0074] The loop step 200 includes step L1 to step L2,

[0075] Step L1: In simulating the PEB process, the overall tendency function, lattice tendency function, and state tendency function that introduce the simulated random number r are used to sequentially confirm the cells where state changes occur, reaction types, and / or diffusion; form a simulation result or trigger a boundary condition to form a simulation result; update and form the overall tendency function, lattice tendency function, and state tendency function according to the simulation result; where 0 < r < 1; introducing a simulated random number less than 1 into the overall tendency function helps to simulate the randomness of the photoresist state change in PEB. With the help of spatial position information, the randomness of the state change at the molecular level of the photoresist during the PEB process can thus be simulated.

[0076] As Figures 2 to 5C shown below, the cells where state changes occur, reaction types, and / or diffusion are introduced sequentially.

[0077] Confirming the cells where state changes occur:

[0078] In one step L1, the simulated random number is multiplied by the overall tendency function to obtain the first selection value for positioning. The first lattice tendency function is subtracted from the first selection value for positioning to obtain the second selection value for positioning. The second lattice tendency function is subtracted from the second selection value for positioning to obtain the third selection value for positioning... until the (i + 1)-th selection value for positioning obtained is below 0, and it is confirmed that the i-th cell has a state change;

[0079] Specifically expressed as a formula, i starts operating from the minimum value of 1 for formula (3) to confirm the cells where state changes occur.

[0080] selector1 = a0 * r,

[0081] selector i+1 = selector i - a i , i = 1,..., N (3)

[0082] selector i+1 is the (i + 1)-th selection value for positioning. When selector i+1 ≤ 0, stop and confirm that the i-th cell has a state change; where a0 is the overall tendency function in the previous step 100 or the overall tendency function updated and formed in step L1, and a i is the lattice tendency function in the previous step 100 or the lattice tendency function of the i-th cell updated and formed in step L1, and N is the number of cells; only through a simple loop subtraction operation can the number of the cell where a state change is about to occur be determined, greatly reducing the time complexity of the calculation.

[0083] As Figure 3 、 Figures 5A to 5BAs shown, the overall tendency function is 33.2. Introduce the simulated random number 0.496, and the product is 16.4672. Subtract successively according to formula (3) and the cell numbers until cell #3 (corresponding to Figure 3 cell 13 in it) to get 33.2 * 0.496 - 6.5 - 5.5 - 12.3 = -7.8328 ≤ 0, then confirm that the state of cell 13 has changed.

[0084] Determine the type of state change in the i-th cell where the state change occurs:

[0085] Locate the (i + 1)-th selection value selector i+1 Set it as the M-th selection value in the steady state. In the i-th cell, add the M-th state tendency function to the M-th selection value in the steady state to get the (M - 1)-th selection value in the steady state, add the (M - 1)-th state tendency function to the (M - 1)-th selection value in the steady state to get the (M - 2)-th selection value in the steady state... until the (M - J)-th selection value in the steady state obtained is greater than 0. Determine the type of state change of the (M - J + 1)-th state tendency function that occurs in the i-th cell. If the (M - J + 1)-th state tendency function is a reaction, subtract one reaction to update the (M - J + 1)-th state tendency function and / or other state changes in the i-th cell affected by the reaction to form a state tendency function, and use it to update the cell tendency function and the overall tendency function of the i-th cell, and use it to perform the next step L2; it should be noted that, as Figure 2 shown, the so-called being affected by the reaction here means that the reactant or product of the (M - J + 1)-th state change is the reactant of other state changes, resulting in a decrease or increase in the reactant of other state changes, thereby causing changes in the state tendency function, cell tendency function, and overall tendency function.

[0086] Specifically expressed as a formula, j starts the operation from the maximum value M for formula (4) to confirm the type of state change in the i-th cell, and selector i,M is the M-th selection value in the steady state:

[0087] selector i,M = selector i+1 ;

[0088] selector i,j-1 = selector i,j + b j , j = M,...1 (4)

[0089] selector i,j-1 is the (M - J)-th selection value in the steady state. When selector i,j-1 > 0, stop and confirm the state change corresponding to the state tendency function b j in the i-th cell; where, b jis the state tendency function of the i-th cell in the previous step 100 or the state tendency function updated in step L1; M is the sum of the total number of all reaction types and the types of diffusing substances in the three-dimensional data structure; since only a simple loop addition is used, the time complexity of the calculation is greatly reduced. Even if there is an operation to determine the cell number where the state change occurs according to formula (3), since the total number of state changes contained in a single cell is small, it will not increase the order of the time complexity, thus improving the real-time performance of the calculation result output.

[0090] If b j The corresponding reaction is, for example Figures 5A to 5C As shown, subtract one reaction update to form b j and / or other state changes in the i-th cell affected by the reaction to update the state tendency function, and use it to update the cell tendency function and the overall tendency function of the i-th cell, and use it to execute step L2.

[0091] For example Figure 3 、 Figure 5A and Figure 5B As shown, as an example where reaction one does not affect other state changes, the overall tendency function is 33.2. Introduce the simulated random number 0.496, and the product is 16.4672. Subtract successively according to formula (3) and the cell number to cell #3 (corresponding to Figure 3 cell 13 in it) to get 33.2 * 0.496 - 6.5 - 5.5 - 12.3 = -7.8328 ≤ 0, then confirm that the state of cell 13 has changed. According to the operation formula (4) shown by the horizontal arrow, -7.8328 + 0.8 + 0.5 + 1.0 + 2.0 + 8.0 = 4.4672 > 0, then confirm that reaction one occurs in cell 13. When it is confirmed that what occurs is a reaction rather than diffusion, update the state tendency function. As Figure 5B shown, assume that reaction one is a deprotection reaction of a certain type of protected group. The number of this type of protected group in cell 13 decreases by one, and the number of deprotected groups increases by one, and this reaction does not consume photoacid (the number of photoacids is 2). Therefore, subtract the product of one reaction and the number of photoacids from the state tendency function of reaction one, that is, the value of 1.0 * 2 to get 6.0. Since the number of photoacids does not change and does not affect the remaining reactions and diffusion in this cell, then update the cell tendency function of cell 13 to 10.3, and update the overall tendency function by subtracting the cell tendency function of cell 13 before the reaction from the overall tendency function before the reaction and then adding the updated cell tendency function of cell 13 after the reaction to form the overall tendency function 31.2.

[0092] For example Figure 3 、 Figure 5CAs shown, as an example of the influence of Reaction 2 on other state changes, the overall tendency function is 33.2. Introduce the simulated random number 0.685, and the product is 22.742. Subtract successively according to Formula (3) and the cell numbers until cell #3 (corresponding to Figure 3 Cell 13 in Figure 5C ), and we get 33.2 * 0.685 - 6.5 - 5.5 - 12.3 = -1.558 ≤ 0. Then it is confirmed that the state of Cell 13 has changed. According to the operation formula (4) shown by the horizontal arrow, -1.558 + 0.8 + 0.5 + 1.0 = 0.742 > 0, so it is confirmed that Reaction 2 occurs in Cell 13. When it is confirmed that a reaction rather than diffusion occurs, as Figure 5C shown, assume that Reaction 2 is the loss of photoacid. If it is a unary reaction, the state tendency function of Reaction 2 with a reaction coefficient of 0.5 minus the value of 0.5 * 1 of the first reaction gives 0.5, and the state tendency function of Reaction 2 is updated to 0.5. Since the number of photoacids decreases by one, the state tendency functions of the reactions and diffusions related to photoacids in Cell 13 need to be updated accordingly. For example, in this example

[0093] shown in Cell 13, the state tendency functions of Reaction 1, Diffusion 1, and Reaction 3 are updated to 4.0, 1.0, and 0.4 respectively. Furthermore, the cell tendency function of Cell 13 is updated to 6.4. Subtract the cell tendency function of Cell 13 before the reaction from the overall tendency function before the reaction and then add the updated cell tendency function of Cell 13 after the reaction to update the overall tendency function to 27.3.

[0093] Or the cell where diffusion is confirmed, the diffusion direction and the target cell:

[0094] If the (M - J + 1)-th state tendency function is diffusion, set the value selected for the stationary state at M - J as the first diffusion selection value;

[0095] In the i-th cell, subtract the first diffusion tendency function from the first diffusion selection value to get the second diffusion selection value; subtract the second diffusion tendency function from the second diffusion selection value to get the third diffusion selection value... until the (p + 1)-th diffusion selection value is below 0. Then the diffusion direction of the p-th diffusion tendency function is the diffusion direction of the i-th cell and the target cell it points to is confirmed. Transfer the p diffusion tendency functions of a diffusion substance of the (M - J + 1)-th state tendency function to the target cell, update the (M - J + 1)-th state tendency functions of the i-th cell and the target cell and / or update the state tendency functions of other state changes affected by the diffusion substance in the i-th cell and the target cell, and update the cell tendency functions and the overall tendency function of the i-th cell and the target cell with them, and start step L2; It should be noted that, as Figure 2As shown, the diffusing substance affecting here refers to the diffusing substance of the (M - J + 1)-th state propensity function, which is the reactant of other state changes, resulting in the decrease (such as the i-th cell in this embodiment) or increase (such as the target cell in this embodiment) of the reactants of other state changes, thereby causing changes in the state propensity function, the lattice propensity function, and the overall propensity function.

[0096] Specifically expressed as a formula, if b j corresponds to diffusion, k starts operating the formula (5) from the minimum value of 1 to confirm the diffusion direction of the i-th cell, selector i,j-1,1 is the first selected value for fixed diffusion:

[0097] selector i,j-1,1 = selector i,j-1

[0098] selector i,j-1,k+1 = selector i,j-1,k - c k , k = 1, … p (5)

[0099] When selector i,j-1,k+1 ≤ 0, stop, confirm the diffusion propensity function c k of the corresponding diffusing substance, and the corresponding diffusing substance will diffuse to c k (corresponding to or equal to b x , b y , or b z ) corresponding diffusion direction, that is, diffuse to the target cell; retrieve the p diffusion propensity functions of a diffusing substance of the state propensity function b j and assign them to the target cell, and update the state propensity function b j of the i-th cell and the target cell respectively, the lattice propensity function, and execute step L2 with them. It should be noted that if the diffusing substance is also involved in other state changes in the i-th cell except for this diffusion, and since the types of state propensity functions of all cells are the same, then the state propensity functions involving this diffusing substance in the i-th cell and the target cell are updated simultaneously. Since only a simple loop subtraction is used, the time complexity of the calculation is greatly reduced. Since the total number of state changes included in the total number of diffusion direction changes in a single cell is small, and the maximum value of the diffusible directions in a single cell is a fixed value p, the order of magnitude of the time complexity will not be increased, thereby improving the real-time performance of the calculation result output.

[0100] As Figure 3 , Figures 4A to 4B shown, cell #3 (corresponding to Figure 3In cell 13), the p-value is 6, the simulated random number r is 0.635. According to the operation formula (3) shown by the vertical arrow, 33.2 * 0.635 - 6.5 - 5.5 - 12.3 = -3.218 ≤ 0 to confirm that cell #3 (corresponding to Figure 3 in cell 13) has a state change. According to the operation formula (4) shown by the horizontal arrow, -3.218 + 0.8 + 0.5 + 1.0 + 2.0 = 1.082 > 0, then it is confirmed that diffusion one occurs in cell 13. According to the vertical arrow operation formula (5), 1.082 - 0.24 - 0.24 - 0.4 - 0.4(y-) = -0.198 ≤ 0, then it is confirmed that diffusion one occurs in cell 13, and the direction is along the reverse direction of the y-axis, that is, the adjacent target cell 14 (corresponding to Figure 4A in cell #4). The six diffusion tendency functions of a diffusion substance included in the diffusion one state tendency function are retrieved and assigned to the target cell 14, that is, as Figure 4B shown, the target cell 14 obtains the value combination (0.12x+, 0.12x-, 0.20y+, 0.20y-, 0.18z+, 0.18z-) in the state tendency function of diffusion one occurring in cell 13. Assuming that diffusion one is the diffusion of photoacid, since one photoacid in cell 13 leaves and enters cell 14, then the number of photoacids in cell 13 decreases by one. Not only the diffusion tendency function of one diffusion substance needs to be retrieved accordingly, but also the state tendency functions of the reactions and diffusions related to photoacid in cell 13 need to be updated accordingly. For example, in this example Figure 4B shown, the state tendency functions of reaction one, reaction two, and reaction three in cell 13 are updated to 4.0, 0.5, and 0.4 respectively. At the same time, since the number of photoacids in cell 14 increases by one, not only the diffusion tendency function of one diffusion substance needs to be assigned to cell 14 accordingly, but also the state tendency functions of the reactions and diffusions related to photoacid in cell 14 need to be updated accordingly. For example, in this example Figure 4B shown, the state tendency functions of reaction one and reaction two in cell 14 are updated to 4.0 and 1.0 respectively. Since cell 14 does not contain the diffusion substance B corresponding to diffusion two, reaction three remains 0. At the same time, update the cell tendency functions of cell 13 and cell 14. Subtract the cell tendency function of cell 13 before diffusion and the cell tendency function of cell 14 before diffusion from the overall tendency function before diffusion, and then add the updated cell tendency function of cell 13 after diffusion and the updated cell tendency function of cell 14 after diffusion. The updated overall tendency function is 30.8.

[0101] The above technical solution uses a hierarchical traversal method to first determine the cells where state changes will occur, then determine the types of state changes that occur in these cells. And when the type of state change that occurs in a cell is diffusion, further determine the direction of diffusion of the cell. By using only one random number, it realizes the real-time high-precision simulation of the random reaction-diffusion phenomenon in the PEB process at the molecular level and outputs the states of side chain groups in real time while maintaining a low time complexity.

[0102] When the state change that occurs in a cell where a state change occurs is diffusion, determine whether the diffusion leaves the photoresist film. If so, trigger the execution of boundary conditions to form a simulation result. Among them, corresponding boundary conditions can be set for the cells located on the surface 1 of the three-dimensional data structure, such as Figure 3 As shown, if the three-dimensional data structure 1 generally has the three-dimensional shape of a photoresist film and can be regarded as a hexahedron, then at least one face of the cells 12, 13, and 14 located on the surface of the hexahedron is on the boundary of the three-dimensional shape of the entire photoresist film. The cells 13 and 14 located on the edges but not the corners of the hexahedron of the three-dimensional data structure 1 have two faces on the boundary of the three-dimensional data structure 1 of the entire photoresist film. The cells (not shown) located on the surface of the hexahedron of the three-dimensional data structure 1 and at the 8 corners of the hexahedron have three faces on the boundary of the three-dimensional data structure 1 of the entire photoresist film. The boundary conditions can be set as reflection boundary conditions or periodic boundary conditions. The reflection boundary condition is that the diffusible substance stops or reflects at the junction of the photoresist film and the non-photoresist film. The periodic boundary condition is that when the diffusible substance leaves the photoresist film and is defined as the range of the three-dimensional data structure 1, it enters the three-dimensional data structure 1 from the symmetric position of the departure point.

[0103] It should be noted that the simulation random number in the loop step 200 needs to be reselected each time. Since the state propensity function of the same cell always tends to decrease whether a reaction or diffusion occurs, in the case of exhaustive simulation, the state propensity functions of each cell will tend to 0, so that a complete simulation structure can be obtained.

[0104] The applicant also designed a method to save the information data of protected and deprotected groups by exchanging the storage space positions of the information data of the groups in the deprotection reaction, without introducing new storage space, which reduces the space complexity. Such as Figure 6As shown, the number of a certain type of protected group in the cell where the state change occurs is q, and the total number of protected and deprotected groups of this type is s. When the corresponding state change occurs to the protected groups of this type, a protected group of this type can be randomly selected for the simulation reaction. At the same time, the information data of the reacting group is exchanged with the information data in the original storage space and the storage space with the address q - 1. At this time, the number of protected groups of this type is q - 1, and the number of deprotected groups of this type is s - q + 1. At this time, the storage spaces from address 0 to q - 2 store the information data of the protected groups of this type, and the storage spaces from address q - 1 to s - 1 store the information data of the deprotected groups of this type.

[0105] Step L2: Calculate the time τ of the next state change using formula (1) m :

[0106]

[0107] where m is the serial number of the next state change; R m is the timing random number of the next state change, and the value range is 0 < R m < 1; a i is the lattice tendency function updated in step L1, N is the number of cells, and i takes values of 1 ≤ i ≤ N, is the overall tendency function updated in step L1.

[0108] Preferably, before the loop step 200, it also includes calculating the time τ1 of the first state change using formula (2):

[0109]

[0110] R1 is the random number of the first state change, and the value range is 0 < R1 < 1; a i is the lattice tendency function in the pre-step 100, N is the number of cells, and i takes values of 1 ≤ i ≤ N, is the overall tendency function in the pre-step 100.

[0111] The method for calculating the state change time of the photoresist in PEB in real time according to the present invention can accurately simulate the random reaction diffusion phenomenon in the PEB process at the molecular level and output the side chain group state in real time. By adopting a simple loop of "positive subtraction - negative addition - positive subtraction" traversal, the calculation complexity is greatly reduced, and the PEB working hours can be quickly simulated and calculated and output in real time. It has strong real-time performance and is more conducive to the processing of high-precision integrated circuits.

[0112] Based on the present application, those skilled in the art should understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number and aspects described herein can be used to implement the device and / or practice the method. Additionally, this device and / or this method can be implemented using other structures and / or functionality in addition to one or more of the aspects described herein.

[0113] Those skilled in the art know that in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to achieve the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a kind of hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structures within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as either software modules for implementing the method or structures within the hardware component.

[0114] It should be noted that the above-mentioned embodiments can be freely combined as needed. The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for calculating the time of change in the state of photoresist in PEB in real time, characterized in that, Including, Pre - step: Confirm the overall tendency function of the three - dimensional data structure with a lattice tendency function that evenly or unevenly divides the three - dimensional data structure of photoresist film information data configured to at least include spatial position information into several cells and a state tendency function of the state change of the cells; the spatial position information at least includes the spatial position information of the side - chain groups on the resin polymer chains in the photoresist, the distribution positions of photo - acids and base neutralizers; the state change types include reaction types and diffusion; Loop steps L1 - L2, Step L1: In the simulated PEB process, successively confirm the cells where state changes occur, reaction types, and / or diffusion with the overall tendency function, lattice tendency function, and state tendency function that introduce the simulated random number r; form a simulation result or trigger boundary conditions to form a simulation result; update to form the overall tendency function, lattice tendency function, and state tendency function according to the simulation result; where, 0 < r < 1; Step L2: Calculate the time τ of the next state change using Equation (1) m :[[-END]] where m is the serial number of the next state change; R m is the timing random number of the next state change, with a value of 0 < R m < 1; a i is the lattice tendency function updated and formed in step L1, N is the number of cells, and i takes values of 1 ≤ i ≤ N, is the overall tendency function updated and formed in step L1.

2. The method according to claim 1, characterized in that, Before the loop step, it also includes calculating the time τ1 of the first state change using formula (2): R1 is a random number for the first state change, with a value of 0 < R1 < 1; a i is the lattice tendency function in the previous step, N is the number of cells, and i takes values of 1 ≤ i ≤ N, is the overall tendency function in the previous step.

3. The method according to claim 1, characterized in that, The types and sorting of the state tendency functions of each cell are the same.

4. The method according to claim 1, characterized in that, The control time limit is 30 seconds to 180 seconds.

5. The method according to claim 1, characterized in that, The boundary conditions include reflection boundary conditions or periodic boundary conditions.

6. The method according to claim 1, characterized in that, In step L1, i starts operating formula (3) from the minimum value of 1 to confirm the cells where state changes occur, selector1 = a0*r, selector i+1 = selector i -a i , i = 1, … N (3) When selector i+1 stops when ≤ 0, and confirm that the state of the i-th cell will change; where a0 is the overall tendency function in the previous step or the overall tendency function formed by the update in L1, a i is the cell tendency function of the i-th cell in the previous step or the cell tendency function of the i-th cell formed by the update in L1, and N is the number of cells; j starts operating formula (4) from the maximum value M to confirm the type of state change in the i - th cell, selector i,M = selector i+1 ; selector i,j-1 = selector i,j + b j , j = M, … 1 (4) Stop when selector i,j-1 > 0, and confirm the state change corresponding to the state tendency function b j in the i-th cell; where b j is the state tendency function of the i-th cell in the previous step or the state tendency function updated in step L1; M is the sum of the total number of reaction types and the types of diffusing substances in the three-dimensional data structure; If b j The corresponding one is the reaction, and the first reaction update is subtracted to form b j And / or other state changes in the i-th cell affected by the reaction are updated to form a state tendency function, and the cell tendency function and the overall tendency function of the i-th cell are updated with it, and step L2 is executed with it; If b j The corresponding one is diffusion, and k starts from the minimum value of 1 to calculate formula (5) to confirm the diffusion direction of the i-th cell: selector i,j-1,1 = selector i,j-1 selector i,j-1,k+1 = selector i,j-1,k -c k , k = 1, … p (5) When selector i,j-1,k+1 Stop when ≤0 and confirm the diffusion function c k The corresponding diffused substance is directed to c k The target cell diffuses in the corresponding diffusion direction; updates the state tendency function of the diffusion of the i-th cell and the target cell and / or updates the state tendency function of other state changes affected by the diffused substance in the i-th cell and the target cell, and uses it to update the grid tendency function and the overall tendency function of the i-th cell and the target cell, and uses it to execute step L2.

7. The method according to claim 6, characterized in that, All cells are hexahedrons, and the p value is 6; or, The cells are tetrahedrons or octahedrons, and the corresponding p values are 4 or 8.

8. The method according to claim 1, characterized in that, The reaction includes group de - protection, acid - base neutralization, or acid loss.

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