Method for improving MB-OPC convergence
By considering fragment interactions in the OPC matrix model and optimizing fragment movement using the gradient descent algorithm, the problem of insufficient convergence in the MB-OPC correction algorithm is solved, achieving higher convergence and accuracy.
Patent Information
- Application Number
- CN202411347902.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-25
- Publication Date
- 2025-01-10
Smart Images
Figure CN119294075A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of semiconductor technology, and in particular to a method for improving the convergence of MB-OPC (model-based OPC). Background Art
[0002] With the continuous development of wafer foundry process technology, the feature size on the node of the logic device is close to or even smaller than the wavelength of the light wave used in the photolithography process. According to the principle of light wave diffraction and interference, the light wave will diffract when passing through the mask, and interference will occur at different positions of the mask. Therefore, the actual light intensity distribution projected onto the silicon wafer is the result of the superposition of these diffracted interference light waves, which is not exactly the same as the mask pattern. This phenomenon of deviation between the photolithography pattern and the mask pattern due to light wave diffraction and interference is called the optical proximity effect (OPE: Optical Proximity Effect). In the photolithography process, the optical proximity effect is inevitable. The existing method is to use optical proximity correction (OPC) technology to minimize the deformation and deviation of the mask pattern projected onto the silicon wafer pattern as much as possible, so that the exposed pattern meets the design requirements.
[0003] The existing MB-OPC divides the target pattern into fragments, uses the optical imaging model to optimize the mask pattern, and verifies the final correction quality through the evaluation function during the optimization process. The calculation formula is: Among them, E fi is the edge placement error (EPE) of each segment. The closer the absolute value of EPE is to 0, the closer the pattern after exposure is to the design pattern. The existing MB-OPC correction algorithm obtains the offset of the corresponding segment by solving the equation movement = EPE * feedback. Since the algorithm only considers the impact of the current segment on EPE during the correction process, but ignores the impact of the offset of other segments on the current EPE, and the feedback value is manually defined, the correction result cannot achieve optimal convergence. Summary of the invention
[0004] In view of the above-mentioned shortcomings of the prior art, the purpose of the present application is to provide a method for improving the convergence of MB-OPC, so as to solve the problem that the MB-OPC correction algorithm in the prior art does not consider the influence of the interaction between each fragment, resulting in the correction result failing to achieve optimal convergence.
[0005] To achieve the above objectives and other related objectives, the present application provides a method for improving MB-OPC convergence, including:
[0006] Step 1: Perform conventional MB-OPC on the target graphic, output the initial OPC graphic and record the corresponding EPE value of each segment;
[0007] Step 2: Mark each fragment;
[0008] Step 3, move each segment of the initial OPC graph by a certain distance in turn, record the updated EPE value of each segment, and then restore to the initial state;
[0009] Step 4, calculate the OPC sensitivity matrix parameters and establish the OPC matrix model;
[0010] Step 5: Set the initial movement amount, gradient step size and number of iterations of each segment;
[0011] Step 6, calculating the gradient value of each segment;
[0012] Step 7, continuously update the movement amount of each segment through the gradient descent method and calculate the OPC evaluation function;
[0013] Step 8, judging whether the number of iterations is met;
[0014] Step nine, bringing the fragment movement amount corresponding to the minimum value of the OPC evaluation function into the correction program to perform OPC.
[0015] Preferably, in step three, each fragment is moved in sequence from small to large according to the number of the label of each fragment.
[0016] Preferably, the movement amount of each segment is the same, and the value of the movement amount is 1 nm.
[0017] Preferably, according to the EPE values of each segment recorded in step 1 and step 3, the OPC sensitivity matrix parameters are calculated by the following formula:
[0018] δ i,n =(E k -E i ) / Δf
[0019] Among them, E i is the initial EPE value of the i-th segment; E k is the EPE value of the i-th fragment after the fragment is moved; Δf is the movement amount of the fragment; when Δf is 1nm, δ i,n is the change in EPE of the nth fragment after moving the ith fragment by 1 nm.
[0020] Preferably, the OPC matrix model expression is:
[0021]
[0022] Among them, EPE i is the EPE value of each fragment after conventional MB-OPC; δ i,nis the OPC sensitivity matrix parameter; is the movement amount of the nth fragment calculated by the m-times gradient descent method; is the final EPE value of the nth segment after m times of gradient descent calculation.
[0023] Preferably, in step five, the initial movement amount of each segment is set according to the initial EPE value of each segment, and the value range of the initial movement amount is set to [-1nm, 1nm].
[0024] Preferably, in step five, the gradient step size is set to 0.01, and the number of iterations is set within the range of [70, 180].
[0025] Preferably, in step seven, the iterative calculation formula of the gradient descent method is as follows:
[0026]
[0027] Where k is 0, 1, 2, ..., the number of iterations set; step is the gradient step size; is the gradient of the i-th segment, where i is 1, 2, …, n.
[0028] Preferably, in step seven, the updated movement amount of each segment is substituted into the OPC matrix model to calculate the OPC evaluation function after each iterative calculation. The OPC evaluation function expression is:
[0029]
[0030] Among them, EPE i is the EPE value of each fragment after conventional MB-OPC; δ i,n is the OPC sensitivity matrix parameter; is the movement amount of the nth fragment calculated by the m-times gradient descent method; is the final EPE value of the nth segment after m times of gradient descent calculation.
[0031] Preferably, in step eight, if the k value is equal to the set number of iterations, continue with step nine; if the k value is less than the set number of iterations, repeat steps six and seven.
[0032] As described above, the method for improving the convergence of MB-OPC provided in the present application has the following beneficial effects: on the basis of the existing MB-OPC, the influence of the interaction between each fragment is incorporated into the OPC matrix model during the OPC correction process, and the optimal fragment movement amount is calculated by the gradient descent algorithm to achieve the optimization of the OPC evaluation function, thereby further improving the convergence of MB-OPC and reducing verification errors. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] In order to more clearly illustrate the specific implementation methods of the present application or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.
[0034] Figure 1 (a) is a comparison chart showing the EPE (absolute value) of four fragments (fragment 1, 2, 3, 4) obtained based on the existing method / the method provided by this application;
[0035] Figure 1 (b) is a comparison diagram showing the simulation fitting graphs obtained based on the existing method / the method provided by the present application;
[0036] Figure 2 A flow chart showing a method for improving MB-OPC convergence provided by an embodiment of the present application;
[0037] Figure 3 A schematic diagram showing an initial OPC graph output after implementing step 1 and its corresponding simulation result based on the method for improving MB-OPC convergence provided by an embodiment of the present application;
[0038] Figure 4 A schematic diagram showing the method for improving MB-OPC convergence provided in an embodiment of the present application, in which step 2 is implemented to mark each segment;
[0039] Figure 5 A schematic diagram showing the change process of the OPC graph during the implementation of step three of the method for improving MB-OPC convergence provided in an embodiment of the present application is shown;
[0040] Figure 6 Shown is a schematic diagram of an OPC graph output after implementing step nine and its corresponding simulation result based on the method for improving MB-OPC convergence provided by an embodiment of the present application. DETAILED DESCRIPTION
[0041] The following describes the implementation of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. The present application can also be implemented or applied through other different specific implementations, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.
[0042] The following will be combined with the accompanying drawings to clearly and completely describe the technical solutions in this application. Obviously, the described embodiments are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.
[0043] In the description of the present application, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating directions or positional relationships, are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second", and "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.
[0044] In the description of this application, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, it can also be the internal connection of two components, it can be a wireless connection, or it can be a wired connection. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood according to specific circumstances.
[0045] In addition, the technical features involved in the different embodiments of the present application described below can be combined with each other as long as they do not conflict with each other.
[0046] The existing MB-OPC correction process does not consider the mutual influence between each fragment, resulting in the final OPC correction result failing to achieve a good convergence effect.
[0047] In order to solve this problem, the present application provides a method for improving the convergence of MB-OPC, by integrating the influence of the interaction between each fragment into the OPC matrix model, and solving the fragment movement amount corresponding to the optimal OPC evaluation function through the gradient descent algorithm, so as to further improve the convergence of OPC, reduce the number of verification errors, and improve work efficiency.
[0048] like Figure 1 (a) and Figure 1As shown in (b), the EPE values of the four fragments (fragment 1, 2, 3, and 4) of the existing MB-OPC are -0.42nm, -0.116nm, -0.104nm, and -0.08nm, respectively, and the evaluation function value is 0.0075. Based on the method for improving the convergence of MB-OPC provided in the present application, the EPE values of the four fragments (fragment 1, 2, 3, and 4) are 0.33nm, -0.085nm, -0.145nm, and 0.0416nm, respectively, and the evaluation function value is 0.0027. Therefore, the evaluation function value obtained based on the method for improving the convergence of MB-OPC provided in the present application is closer to 0, and the OPC convergence is higher.
[0049] See also Figure 2 , which shows a flow chart of a method for improving MB-OPC convergence provided in an embodiment of the present application.
[0050] like Figure 2 As shown, the method for improving the convergence of MB-OPC includes the following steps:
[0051] Step 1: Perform conventional MB-OPC on the target graphic, output the initial OPC graphic and record the corresponding EPE value of each segment;
[0052] Step 2: Mark each fragment;
[0053] Step 3, move each segment of the initial OPC graph by a certain distance in turn, record the updated EPE value of each segment, and then restore to the initial state;
[0054] Step 4, calculate the OPC sensitivity matrix parameters and establish the OPC matrix model;
[0055] Step 5: Set the initial movement amount, gradient step size and number of iterations of each segment;
[0056] Step 6, calculating the gradient value of each segment;
[0057] Step 7, continuously update the movement amount of each segment through the gradient descent method and calculate the OPC evaluation function;
[0058] Step 8, judging whether the number of iterations is met;
[0059] Step nine, bringing the fragment movement amount corresponding to the minimum value of the OPC evaluation function into the correction program to perform OPC.
[0060] In step one, Figure 3For example, conventional MB-OPC is implemented on the target graphic (target), the initial OPC graphic (CT_OPC) is output, and the EPE values of the four segments (7.2, 6.94331, 7.30731, 7.16263) are recorded.
[0061] In step 2, Figure 4 For example, there are four fragments located on the four sides of the square. Starting from the fragment located on the upper side of the square, the four fragments are marked as mk1, mk2, mk3, and mk4 in a clockwise direction.
[0062] In step three, Figure 5 For example, first move fragment 1 (fragment1, labeled as mk1), record the EPE values of the four fragments (6.04257, 6.6, 6.9, 6.7), and restore it to its original state; then, move fragment 2 (fragment2, labeled as mk2), record the EPE values of the four fragments (6.8, 5.8, 6.76389, 6.8), and restore it to its original state; then, move fragment 3 (fragment3, labeled as mk3), record the EPE values of the four fragments (6.9, 6.6, 6.0, 6.74765), and restore it to its original state; finally, move fragment 4 (fragment4, labeled as mk4), record the EPE values of the four fragments (6.8, 6.81644, 6.86815, 5.8), and restore it to its original state.
[0063] Each segment is moved in order from small to large according to the number of each segment, and the movement amount of each segment is the same, and the typical value of the movement amount is 1 nm.
[0064] In step 4, based on the EPE values of each segment recorded in steps 1 and 3, the OPC sensitivity matrix parameter δ is calculated by the following formula: i,n :
[0065] δ i,n =(E k -E i ) / Δf (1)
[0066] Among them, E i is the initial EPE value of the i-th segment; E k is the EPE value of the i-th fragment after the fragment is moved; Δf is the movement amount of the fragment; when Δf is 1nm, δ i,n is the change in EPE of the nth fragment after moving the ith fragment by 1 nm.
[0067] The OPC matrix model expression is:
[0068]
[0069] Simplifying formula (2) into:
[0070]
[0071] Among them, EPE i is the EPE value of each segment after conventional MB-OPC, Figure 3 For example, the EPE value of each recorded segment is EPE i ; δ i,n is the OPC sensitivity matrix parameter, calculated by formula (1); is the movement amount of the nth fragment calculated by the m-times gradient descent method; is the final EPE value of the nth segment after m times of gradient descent calculation.
[0072] In step 5, the initial movement of each segment is set according to the initial EPE value of each segment. For the convenience of calculation, the initial movement of each segment can be set to the same value. Since OPC is a process of fine-tuning the mask size, the initial movement value should not be too large. The value range of the initial movement is usually set to [-1nm, 1nm]. The gradient step size is recommended to be set to 0.01, and the number of iterations can be set in the range of [70, 180].
[0073] In step 6, the partial derivatives of each segment of the OPC matrix model are calculated according to formula (2) to obtain the corresponding gradient value
[0074] In step seven, the iterative calculation formula of the gradient descent method is as follows:
[0075]
[0076] Where k is 0, 1, 2, ..., the number of iterations set; step is the gradient step size; is the gradient of the i-th segment, where i is 1, 2, …, n.
[0077] The movement amount of each fragment is continuously updated iteratively through formula (4), and then the updated movement amount of each fragment is substituted into formula (3) to calculate the OPC evaluation function after each iterative calculation.
[0078] The OPC evaluation function expression is:
[0079]
[0080] In step eight, if the k value is equal to the set number of iterations, continue with step nine; if the k value is less than the set number of iterations, repeat steps six and seven.
[0081] In step nine, the segment movement amount corresponding to the minimum value of all OPC evaluation functions obtained by iterative calculation is brought into the correction program to perform OPC.
[0082] Compared with the traditional MB-OPC, after the optimization of the method for improving the convergence of MB-OPC provided by this application, the average EPE value decreased by 13.6% and the OPC evaluation function decreased by 41%. Figure 6 For example, the obtained OPC graph is more convergent and has higher accuracy.
[0083] It should be noted that the illustrations provided in this embodiment are only used to illustrate the basic concept of the present application in a schematic manner. Therefore, the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.
[0084] In summary, the method for improving the convergence of MB-OPC provided by the present application, based on the existing MB-OPC, incorporates the influence of the interaction between each fragment into the OPC matrix model during the OPC correction process, and calculates the optimal fragment movement amount through the gradient descent algorithm to achieve the optimization of the OPC evaluation function, thereby further improving the convergence of MB-OPC and reducing verification errors. Therefore, the present application effectively overcomes various shortcomings in the prior art and has a high industrial utilization value.
[0085] The above embodiments are merely illustrative of the principles and effects of the present application and are not intended to limit the present application. Anyone familiar with the technology may modify or change the above embodiments without violating the spirit and scope of the present application. Therefore, all equivalent modifications or changes made by a person of ordinary skill in the art without departing from the spirit and technical ideas disclosed by the present invention shall still be covered by the claims of the present application.
Claims
1. A method for improving MB-OPC convergence, characterized in that: The method comprises: Step 1: Perform conventional MB-OPC on the target graphic, output the initial OPC graphic and record the corresponding EPE value of each segment; Step 2, marking each of the fragments; Step 3, moving each segment of the initial OPC graph by a certain distance in turn, and recording the updated EPE value of each segment, and then restoring the initial state; Step 4, calculate the OPC sensitivity matrix parameters and establish the OPC matrix model; Step 5, setting the initial movement amount, gradient step size and number of iterations of each segment; Step six, calculating the gradient value of each segment; Step 7, continuously updating the movement amount of each segment by gradient descent method and calculating the OPC evaluation function; Step 8, determining whether the number of iterations is met; Step nine, bringing the fragment movement amount corresponding to the minimum value of the OPC evaluation function into the correction program to perform OPC.
2. The method according to claim 1, characterized in that In the step three, the fragments are moved in sequence from small to large according to the numbers of the labels of the fragments.
3. The method according to claim 1 or 2, characterized in that: The movement amount of each segment is the same, and the value of the movement amount is 1 nm.
4. The method according to claim 1, characterized in that: According to the EPE values of the segments recorded in step 1 and step 3, the OPC sensitivity matrix parameters are calculated by the following formula: δ i，n =(And k -AND i ) / Δf Among them, E i is the initial EPE value of the i-th segment; E k is the EPE value of the i-th fragment after the fragment is moved; Δf is the movement amount of the fragment, when Δf is 1nm, δ i，n is the change in EPE of the nth fragment after moving the ith fragment by 1 nm.
5. The method according to claim 1, characterized in that The OPC matrix model expression is: Among them, EPE i is the EPE value of each fragment after conventional MB-OPC; δ i，n is the OPC sensitivity matrix parameter; is the movement amount of the nth fragment calculated by the m-times gradient descent method; is the final EPE value of the nth segment after m times of gradient descent calculation.
6. The method according to claim 1, characterized in that In the step five, the initial movement amount of each segment is set according to the initial EPE value of each segment, and the value range of the initial movement amount is set to [-1nm, 1nm].
7. The method according to claim 1, characterized in that In step five, the gradient step size is set to 0.01, and the number of iterations is set within the interval range of [70, 180].
8. The method according to claim 1, characterized in that In step seven, the iterative calculation formula of the gradient descent method is as follows: Where k is 0, 1, 2, ..., the number of iterations set; step is the gradient step size; is the gradient of the i-th segment, where i is 1, 2, …, n.
9. The method according to claim 1, characterized in that: In step seven, the updated movement amount of each segment is substituted into the OPC matrix model to calculate the OPC evaluation function after each iterative calculation. The OPC evaluation function expression is: Among them, EPE i is the EPE value of each fragment after conventional MB-OPC; δ i,n is the OPC sensitivity matrix parameter; is the movement amount of the nth fragment calculated by the m-times gradient descent method; is the final EPE value of the nth segment after m times of gradient descent calculation.
10. The method according to claim 8, characterized in that In step eight, if the k value is equal to the set number of iterations, continue with step nine; if the k value is less than the set number of iterations, repeat steps six and seven.