Negative development photoresist shrinkage effect modeling method based on lattice spring model
By simulating the shrinkage effect of negatively developed photoresist using a lattice spring model, the problem of photoresist shrinkage error in existing technologies is solved, achieving efficient and accurate simulation of photoresist shrinkage effect and improving the imaging accuracy of integrated circuit manufacturing.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-10
- Publication Date
- 2026-04-10
AI Technical Summary
The lack of effective simulation of the shrinkage effect of negatively developed photoresist in existing technologies leads to errors in key positions of the photoresist, affecting high-fidelity imaging in integrated circuit manufacturing.
By employing a lattice spring model-based approach, the concentration distribution of protective sites in the discrete lattice of photoresist is calculated through the exposure, baking, reaction, and diffusion process. The mapping factor is then calculated using lattice spring theory to establish a model of the photoresist shrinkage effect, thereby simulating the entire process from exposure to development.
It achieves accurate simulation of the shrinkage effect of negatively developed photoresist, improves simulation effect and efficiency, ensures accurate measurement of key dimensions of photoresist, and fills the gap in existing technology.
Smart Images
Figure CN121832205A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of computational lithography technology in integrated circuit manufacturing, and in particular to a method for modeling the shrinkage effect of negative developing photoresist based on a lattice spring model. Background Technology
[0002] In large-scale manufacturing processes at wavelengths of 248nm and 193nm, positive tone development (PTD) chemically amplified photoresists, developed in aqueous solutions, are used. However, as integrated circuit manufacturing processes advance to technology nodes of 14nm and below, high-fidelity imaging of smaller critical dimension (CD) patterns places higher demands on photolithography, prompting researchers to explore negative tone development (NTD), as it is seen as a reliable technique for improving the exposure performance of contact hole and channel patterns in photolithography. Negative tone development is a process technique that combines a bright-field mask, positive photoresist, and an organic developer. Both positive and negative development processes use positive photoresist. The main differences are: 1) Positive development uses traditional alkaline developer, while negative development uses organic developer; 2) In positive development, areas of the photoresist that receive more light energy undergo a chemical reaction and are washed away by the developer, while in negative development, areas that receive less light energy are washed away by the organic developer; 3) Positive development requires a dark-field mask, while negative development requires a bright-field mask. Compared to dark-field masks, bright-field masks offer higher contrast, lower edge roughness, and a larger process window for smaller line and hole patterns.
[0003] Negative development suffers from a severe resist shrinkage effect. This is due to the acid-catalyzed deprotection reaction during the baking stage, which generates volatile byproducts that diffuse to and escape from the photoresist surface. When the voids left by these escaped volatile molecules reach a certain size, collapse occurs, ultimately leading to photoresist volume shrinkage and causing errors in critical locations. Furthermore, photoresist simulations lack modeling methods that consider this shrinkage effect in negative development. Summary of the Invention
[0004] In view of the above analysis, the present invention aims to provide a method for modeling the shrinkage effect of negative developing photoresist based on a lattice spring model, so as to solve the problem of lack of simulation of the shrinkage effect of negative developing photoresist in the prior art.
[0005] The objective of this invention is mainly achieved through the following technical solutions:
[0006] A method for modeling the shrinkage effect of negative photoresist based on a lattice spring model includes the following steps:
[0007] Based on the reaction-diffusion process of exposure and baking, the concentration distribution of protective sites in the discrete lattice of photoresist without considering the shrinkage effect is obtained;
[0008] Based on the lattice spring theory, the mapping factor of each discrete photoresist lattice is calculated considering the photoresist shrinkage effect; the mapping factor is used to represent the transformation relationship before and after considering the photoresist shrinkage effect.
[0009] Based on the mapping factor and the protective site concentration distribution without considering the shrinkage effect, the protective site concentration distribution of the photoresist discrete lattice considering the shrinkage effect is obtained;
[0010] Based on the concentration distribution of the protected sites and the development model that takes into account the shrinkage effect, the post-development profile and the key dimensions for measurement considering the shrinkage effect are obtained.
[0011] Furthermore, the specific steps for calculating the mapping factor for each photoresist discrete lattice include:
[0012] Record the initial position information of each discrete lattice of photoresist obtained after exposure baking simulation processing;
[0013] Calculate the total potential energy of the photoresist system based on the lattice spring theory and the properties of photoresist materials.
[0014] The latest equilibrium position of each lattice after the contraction steady state is determined based on the total potential energy of the system.
[0015] The displacement distance between the latest equilibrium position and the initial position of each lattice is calculated to obtain the mapping factor of each lattice.
[0016] Furthermore, calculating the total potential energy of the photoresist system includes:
[0017] The photoresist discrete lattice is divided into several lattice networks, each of which includes one central lattice, four nearest neighbor lattices, and four second nearest neighbor lattices.
[0018] Based on the lattice spring theory and the properties of photoresist materials, the contribution of lattices at different positions in each lattice network to the potential energy of the central lattice is obtained, and the potential energy of each lattice network is calculated based on the contribution and the position of each lattice.
[0019] The total potential energy of the photoresist system is obtained by summing the potential energies of all lattice networks.
[0020] Furthermore, the contributions include the contributions of the nearest neighbor lattice and the second nearest neighbor lattice to the potential energy of the central lattice, as well as the relevant contributions of the nearest neighbor lattice and the temperature during baking to the central lattice.
[0021] Furthermore, the formula for calculating the total potential energy of the photoresist system is as follows:
[0022]
[0023] Where, r n Indicates the position of the central lattice; This indicates the position of the nearest or second nearest neighbor lattice. This represents the distance between two points after deformation. This represents the initial length between the two corresponding points; The value represents the elastic coefficient between the two corresponding points; T is the temperature during baking; and N represents the total number of photoresist lattice networks.
[0024] Furthermore, the elastic coefficient is calculated based on the following formula using the concentration of the protected sites without considering the contraction effect:
[0025]
[0026] Where a is the scaling factor; m(r) n ), They represent the locations at r respectively n and The concentration of protected sites at the lattice without considering shrinkage effects.
[0027] Furthermore, the latest equilibrium position of each lattice point after the contraction steady state is based on the position of each lattice point when the total potential energy of the system is minimized according to the boundary conditions.
[0028] Furthermore, the boundary conditions include fixing the bottom of the photoresist material so that the bottom edge lattice of the bottom layer of the photoresist lattice network does not participate in deformation.
[0029] Furthermore, the concentration of protected sites for each discrete photoresist lattice, considering the shrinkage effect, is obtained based on the following formula:
[0030] m s (i) = S(i) * m(i),
[0031] Where S(i) represents the mapping factor of the lattice at position i; m s (i) and m(i) represent the concentration of protected sites in the i-position lattice considering and not considering the shrinkage effect, respectively.
[0032] Furthermore, the concentration distribution of protected sites in the discrete lattice of the photoresist, without considering the shrinkage effect, is obtained based on the following formula:
[0033]
[0034] Where H and M represent the concentration distributions of acid molecules and protected sites, respectively; and K4 represents the reaction rate.
[0035] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:
[0036] 1. This invention proposes a photoresist modeling method for negative development shrinkage effect. First, the light intensity distribution is transformed into a protective site concentration distribution using reaction-diffusion theory. Then, the shrinkage effect is simulated using lattice spring theory. Finally, the development profile and critical dimension (CD) are measured using a negative development model. This achieves accurate simulation of the shrinkage effect of negative development photoresist, filling the gap in existing methods for simulating shrinkage effects.
[0037] 2. The proposed photoresist modeling method has a fast calculation speed, which greatly improves the simulation effect and efficiency, and realizes accurate characterization of real photoresist materials.
[0038] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description
[0039] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.
[0040] Figure 1 This is a schematic diagram of the overall process of an embodiment of the present invention;
[0041] Figure 2 This is a schematic diagram of a lattice network according to an embodiment of the present invention;
[0042] Figure 3 This is a schematic diagram showing the displacement changes of the four crystal lattices before and after shrinkage in an embodiment of the present invention;
[0043] Figure 4 This is a simulation result diagram of the area of a densely packed quadrilateral without considering the shrinkage effect in an embodiment of the present invention;
[0044] Figure 5 This is a simulation result diagram of the concentration of protected sites in a dense pattern without considering the shrinkage effect in an embodiment of the present invention;
[0045] Figure 6 This is a simulation result diagram of the development contour of a dense pattern without considering the shrinkage effect in an embodiment of the present invention;
[0046] Figure 7 The simulation results of the area of the densely patterned quadrilateral considering the shrinkage effect are shown in the embodiment of the present invention.
[0047] Figure 8 The simulation results of the concentration of densely patterned protected sites considering the contraction effect are shown in the embodiment of the present invention.
[0048] Figure 9 The simulation result diagram shows the development contour of a dense pattern considering the shrinkage effect in an embodiment of the present invention;
[0049] Figure 10 This is a diagram showing the difference in area between densely patterned quadrilaterals that do not consider the shrinkage effect and those that do consider it in the embodiments of the present invention.
[0050] Figure 11 This is a graph showing the difference in concentration of densely patterned protected sites between embodiments of the present invention that do not consider and do consider the shrinkage effect;
[0051] Figure 12 This is a diagram showing the difference in the development contours of dense patterns that do not consider shrinkage effects compared to embodiments of the present invention.
[0052] Figure 13 The key dimension results of three different sets of graphics selected as test graphics in the embodiments of the present invention are shown. Detailed Implementation
[0053] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.
[0054] A specific embodiment of the present invention discloses a method for modeling the shrinkage effect of negatively developed photoresist based on a lattice spring model, such as... Figure 1 As shown, it includes the following steps:
[0055] Step S1: Based on the reaction diffusion process in the exposure baking simulation, the concentration distribution of protective sites in the discrete lattice of the photoresist without considering the shrinkage effect is obtained;
[0056] Step S2: Calculate the mapping factor of each discrete photoresist lattice considering the photoresist shrinkage effect based on the lattice spring theory; the mapping factor is used to represent the transformation relationship before and after considering the photoresist shrinkage effect.
[0057] Step S3: Based on the mapping factor and the protective site concentration distribution without considering the shrinkage effect, obtain the protective site concentration distribution of the photoresist discrete lattice considering the shrinkage effect;
[0058] Step S4: Based on the concentration distribution of the protected sites and the development model considering the shrinkage effect, obtain the post-development profile and the key measurement dimensions considering the shrinkage effect.
[0059] Using the above method, the light intensity distribution is converted into a photoacid distribution and a protective site concentration distribution through exposure and baking; the mapping factor considering the shrinkage effect is calculated based on the lattice spring theory, and then the protective site concentration distribution after shrinkage is obtained; the development model converts the protective site concentration distribution into the development profile and the corresponding key size value, thereby realizing the accurate simulation of the shrinkage effect of negative development photoresist.
[0060] Specifically, the detailed steps of the exposure and baking simulation in step S1 are as follows:
[0061] Step S11: Based on the photochemical reaction during exposure and baking, the light intensity distribution in the photoresist is converted into a photoacid distribution;
[0062] Because different locations in the photoresist receive different doses of light during exposure, the photoacid generator within the photoresist undergoes a photochemical reaction to produce acid molecules, thereby converting the light intensity distribution into a photoacid distribution. The expression is:
[0063] H = G0(1-e -CIt ),
[0064] Where H is the concentration of acid molecules; G0 is the initial concentration of photoacid generator; I is the light intensity distribution; t is time; and C is the reaction coefficient.
[0065] Step S12: Based on the chemical amplification reaction, the concentration of the protected sites of the photoresist is obtained.
[0066] Specifically, in the high-temperature baking environment, a reaction altering the solubility of the photoresist is induced. The acid molecules generated by the photochemical reaction will partly act as a catalyst in this process and partly as reactants, neutralizing molecules in the acid inhibitor. These two processes occur simultaneously, and both acid molecules and acid inhibitor molecules continuously diffuse from locations of high concentration to locations of low concentration. This process is called a reaction-diffusion process and can be solved simultaneously using the following set of equations:
[0067]
[0068]
[0069] Where H, Q, and M represent the concentration distributions of acid molecules, acid molecule inhibitors, and protective sites (without considering contraction effects), respectively; K quench K4 represents the corresponding reaction rate; D H D represents the diffusion rate of acid molecules. QThe diffusion rate of acid molecule inhibitor molecules; This represents the square operation of the gradient.
[0070] For example, an exposure baking simulation model is established based on the above equations to realize the exposure baking simulation process. By fixing the light source, photolithography system, and various parameters affecting photoresist performance, the light intensity distribution is converted into a photoacid distribution through the exposure baking simulation model. Then, using reaction-diffusion theory, the concentration distribution of protected sites, without considering shrinkage effects, is obtained. Figure 5 As shown.
[0071] It should be noted that the so-called lattice spring theory in step S2 represents the structure of the material as a lattice network composed of nodes and springs, which is used to study the shape change of the material under the action of external conditions. The total potential energy expression of the system is established by integrating the lattice spring theory. Based on the idea that the system is in a steady state when the total potential energy is at its minimum, the latest equilibrium position of each point in the steady state is solved.
[0072] Specifically, a shrinkage simulation model is established based on the lattice network and total potential energy of the system according to the above-mentioned lattice spring theory. The steady-state equilibrium position is solved, and the mapping factor of each discrete photoresist lattice considering the shrinkage effect is calculated using the steady-state equilibrium position and the initial position. The specific steps include:
[0073] Step S21: During the exposure and baking simulation, the photoresist is discretized into individual lattice points (lattices) to obtain the discrete lattice points in the initial state, and the initial position information of each lattice is recorded.
[0074] For example, the discrete lattice points in the initial state are all located in regular positions, such as (0, 0), (0, 1), (1, 1), etc. To facilitate comparison of the shrinkage effect, four adjacent lattice points are grouped together, such as... Figure 3 As shown, the horizontal stripe-shaped lattice points represent the initial state positions. Without considering the shrinkage effect, a set of lattice points forms a square with quadrilaterals of area 1, as shown below. Figure 4 As shown.
[0075] Step S22: Based on the lattice spring theory and the properties of the photoresist material, calculate the total potential energy of the photoresist system based on each lattice point;
[0076] For example, the photoresist discrete lattice is divided into several lattice networks. Within each lattice network, all lattices except the central lattice point can be categorized into nearest-neighbor lattice points and second-nearest-neighbor lattice points based on their distance from the central lattice point. For example... Figure 2 As shown, assuming the central lattice point is n (grid-like), each lattice network, in addition to the central lattice point, also has 4 nearest neighbor lattice points with a distance of 1 (horizontal stripes) and 4 nearest neighbor lattice points with a distance of... The next nearest neighbor lattice points (vertical stripes). Based on lattice spring theory and the properties of photoresist materials, different types of lattice points contribute differently to the total potential energy of the system. Specifically, this includes calculating the potential energy of each lattice network based on the contribution of lattices at different positions within each lattice network to the potential energy of the central lattice and the position of each lattice; the sum of the potential energies of all lattice networks yields the total potential energy of the photoresist system. The contributions include the contributions of the nearest and second nearest neighbor lattices to the potential energy of the central lattice (see the left side of the plus sign in the following formula), and the related contributions of the nearest neighbor lattices and the temperature during baking to the central lattice (see the right side of the plus sign in the following formula). Specifically, this can be calculated using the following expression:
[0077]
[0078] Where, r n Indicates the position of the central lattice; This indicates the position of the nearest or second nearest neighbor lattice. The value of bn to the left of the plus sign ranges from 1 to 8, representing the nearest and second nearest neighbor lattices; the value of bn to the right of the plus sign ranges from 1 to 4, representing the four nearest neighbor lattices. This represents the distance between the central lattice and the nearest or second nearest neighbor lattice after deformation. This represents the initial length between the two corresponding points; The value represents the elastic coefficient between the two corresponding points; T is the temperature during baking (in °F); N represents the total number of photoresist lattice networks.
[0079] It needs to be explained that, Available Perform the calculation; for the nearest neighbor lattice, L is set to 1, and for the second nearest neighbor lattice, L is set to... fscale represents the scaling factor; Available Perform calculations; They represent the locations at r respectively n and The concentration of protected sites in the lattice is denoted by fscale, and 'a' is a scaling factor. Both fscale and 'a' are parameters to be fitted using experimental data. For example, fscale typically ranges from 0.5 to 1, and 'a' ranges from 1 to 50. The specific values are determined based on the actual application to ensure the simulation model conforms to reality.
[0080] Step S23: Based on the total potential energy of the system, solve for the latest equilibrium position of each lattice after the contraction steady state;
[0081] Specifically, boundary conditions are set (such as fixing the bottom of the material so that the bottom edge lattice of the bottom layer of the photoresist lattice network does not participate in deformation), and the system potential energy function is solved according to the system potential energy expression to obtain the position information of the lattice points when the system potential energy is at its minimum (steady state after contraction).
[0082] For example, comparing the positional changes of the same set of lattices at steady state, such as Figure 3 As shown, the positions of the four lattice points with vertical stripes are the latest equilibrium positions. At this point, the area of the quadrilateral considering the contraction effect is as follows: Figure 7 As shown in the figure, a comparative analysis using the area of quadrilaterals yields a graph showing the difference between the areas of quadrilaterals without and with regard to the shrinkage effect, as shown in the figure. Figure 10 As shown.
[0083] Step S24: Calculate the displacement distance between the latest equilibrium position and the initial position for each lattice, where the displacement distance is the mapping factor for each lattice.
[0084] Specifically, in step S3, based on the mapping factor, the concentration of protective sites (inhibitor concentration) after considering the contraction effect is obtained according to the following formula:
[0085] m s (i) = S(i) * m(i),
[0086] Where S(i) represents the mapping factor of the lattice at position i; m s (i) and m(i) represent the concentration of protected sites in the i-position lattice considering and not considering the shrinkage effect, respectively.
[0087] An exemplary schematic diagram of the concentration of protected sites considering the contraction effect is obtained, such as... Figure 8 As shown; a graph illustrating the difference in protective site concentrations without and with regard to contraction effects, as shown. Figure 11 As shown.
[0088] Specifically, in step S4, during the development stage, the Mack model used for the positive development process is inverted to simulate the negative development process. The corresponding development model expression that does not consider the shrinkage effect is as follows:
[0089]
[0090] Among them, R max R min These represent the maximum and minimum developing rates, respectively; a through Calculate M th denoted as the protection site threshold concentration, n represents the dissolution selectivity parameter, which describes the sensitivity of the developer to the photoresist exposure area, and M represents the protection site concentration distribution.
[0091] For example, when considering the shrinkage effect, the concentration of protected sites m at each lattice point is... s(x,y) yields the concentration distribution Ms of the protected sites of the photoresist considering the shrinkage effect. Ms is then input into the negative development model, where M = Ms in the corresponding expression, to obtain the development model considering the shrinkage effect. This leads to the development result profile considering the shrinkage effect and the corresponding CD value.
[0092] Similarly, using m(x,y) of each lattice point, the corresponding protective site concentration distribution M without considering the shrinkage effect is obtained. Inputting the inhibitor concentration distribution without considering the shrinkage effect into the negative development model yields the development result profile without considering the shrinkage effect and the corresponding CD value. A comparison of the photoresist development profiles considering and without considering the shrinkage effect is shown below. Figure 6 and Figure 9 As shown, the contour differences between the two are as follows: Figure 12 As shown, the key dimensions obtained by the above method, taking into account the shrinkage effect, yield more accurate data results.
[0093] To verify the model's effectiveness, three sets of photoresists with different patterns were selected for testing: dense pattern (L38P80), semi-dense pattern (L70P160), and isolated pattern (L50P420).
[0094] Figure 13 The test patterns are shown in key dimension results (in nanometers) for dense, semi-dense, and isolated patterns. Since the key dimension measurement involves measuring the width of the central groove, for example, the width of the central groove for the dense pattern is... Figure 6 and 9 The width of the blue area without photoresist should be increased due to the shrinkage of the photoresist on both sides. Therefore, the method described in this invention can simulate the shrinkage phenomenon of negatively developed photoresist for three different test patterns, demonstrating the universality of the proposed method.
[0095] It should be noted that before mass-producing chips using photoresist, real-world experimental testing needs to be conducted in the manufacturing plant (fab), generating a large number of experimental results. Mass production proceeds only after the testing results meet expectations. The testing phase is costly and time-consuming. By establishing a model using the method described in this invention, the simulation results are made as close as possible to the experimental results, reducing errors, accurately describing the actual situation, and improving efficiency.
[0096] Compared with existing technologies, this embodiment provides a method for modeling the shrinkage effect of negatively developed photoresist based on a lattice spring model. By establishing a complete process flow model of negatively developed photoresist from exposure and baking to development, focusing on the process from baking to development, a shrinkage model is established using lattice spring theory, ultimately simulating the shrinkage effect of negatively developed photoresist. On the one hand, this method fills the gap in existing methods for simulating shrinkage effects, achieving accurate characterization of real photoresist materials; on the other hand, the lattice spring-based photoresist modeling method has a faster calculation speed, greatly improving the simulation effect and efficiency.
[0097] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.
[0098] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for modeling the shrinkage effect of negatively developed photoresist based on a lattice spring model, characterized in that, Includes the following steps: Based on the reaction-diffusion process of exposure and baking, the concentration distribution of protective sites in the discrete lattice of photoresist without considering the shrinkage effect is obtained; Based on the lattice spring theory, the mapping factor of each discrete photoresist lattice considering the photoresist shrinkage effect is calculated separately; The mapping factor is used to represent the conversion relationship before and after considering the photoresist shrinkage effect; Based on the mapping factor and the protective site concentration distribution without considering the shrinkage effect, the protective site concentration distribution of the photoresist discrete lattice considering the shrinkage effect is obtained; Based on the concentration distribution of the protected sites and the development model that takes into account the shrinkage effect, the post-development profile and the key dimensions for measurement considering the shrinkage effect are obtained.
2. The method for modeling the shrinkage effect of negative photoresist based on a lattice spring model according to claim 1, characterized in that, The specific steps for calculating the mapping factor for each discrete photoresist lattice include: Record the initial position information of each discrete lattice of photoresist obtained after exposure and baking simulation processing; Calculate the total potential energy of the photoresist system based on the lattice spring theory and the properties of photoresist materials. The latest equilibrium position of each lattice after the contraction steady state is determined based on the total potential energy of the system. The displacement distance between the latest equilibrium position and the initial position of each lattice is calculated to obtain the mapping factor of each lattice.
3. The method for modeling the shrinkage effect of negative photoresist based on a lattice spring model according to claim 2, characterized in that, The calculation of the total potential energy of the photoresist system includes: The photoresist discrete lattice is divided into several lattice networks, each of which includes one central lattice, four nearest neighbor lattices, and four second nearest neighbor lattices. Based on the lattice spring theory and the properties of photoresist materials, the contribution of lattices at different positions in each lattice network to the potential energy of the central lattice is obtained, and the potential energy of each lattice network is calculated based on the contribution and the position of each lattice. The total potential energy of the photoresist system is obtained by summing the potential energies of all lattice networks.
4. The method for modeling the shrinkage effect of negative photoresist based on a lattice spring model according to claim 3, characterized in that, The contributions include the contributions of the nearest neighbor lattice and the second nearest neighbor lattice to the potential energy of the central lattice, and the relevant contributions of the nearest neighbor lattice and the temperature during baking to the central lattice.
5. The method for modeling the shrinkage effect of negative photoresist based on a lattice spring model according to claim 4, characterized in that, The formula for calculating the total potential energy of the photoresist system is: Where, r n Indicates the position of the central lattice; This indicates the position of the nearest or second nearest neighbor lattice. This represents the distance between two points after deformation. This represents the initial length between the two corresponding points; The value represents the elastic coefficient between the two corresponding points; T is the temperature during baking; and N represents the total number of photoresist lattice networks.
6. The method for modeling the shrinkage effect of negative photoresist based on a lattice spring model according to claim 5, characterized in that, The elastic coefficient is calculated based on the following formula using the concentration of the protected sites without considering the contraction effect: Where a is the scaling factor; m(r) n ), They represent the locations at r respectively n and The concentration of protected sites at the lattice without considering shrinkage effects.
7. The method for modeling the shrinkage effect of negative photoresist based on a lattice spring model according to claim 2, characterized in that, The latest equilibrium position of each lattice point after the contraction steady state is calculated based on the boundary conditions to determine the position of each lattice point when the total potential energy of the system is minimized.
8. The method for modeling the shrinkage effect of negative photoresist based on a lattice spring model according to claim 7, characterized in that, The boundary conditions include fixing the bottom of the photoresist material so that the bottom edge lattice of the bottom layer of the photoresist lattice network does not participate in deformation.
9. A method for modeling the shrinkage effect of negative photoresist based on a lattice spring model according to any one of claims 1-8, characterized in that, The concentration of protected sites for each discrete lattice of the photoresist, taking into account the shrinkage effect, is obtained based on the following formula: m s (i)=S(i)*m(i), Where S(i) represents the mapping factor of the lattice at position i; m s (i) and m(i) represent the concentration of protected sites in the i-position lattice considering and not considering the shrinkage effect, respectively.
10. A method for modeling the shrinkage effect of negative photoresist based on a lattice spring model according to claim 1, characterized in that, The concentration distribution of protected sites in the discrete lattice of the photoresist, without considering the shrinkage effect, is obtained based on the following formula: Where H and M represent the concentration distributions of acid molecules and protected sites, respectively; and K4 represents the reaction rate.