Simulation device

Abstract

This invention provides a simulation device that performs high-speed and precise shape simulations using the voxel method. [Solution] The simulation device includes a simulation execution unit that performs shape simulation using voxels having a first size, and a conversion unit that converts the voxels from which the shape simulation was performed into voxels having a second size smaller than the first size. Preferably, the conversion unit converts the voxels from which the shape simulation was performed into voxels having the second size using surface extraction.

Description

[Technical Field]

[0001] This invention relates to a simulation device that performs high-speed and precise shape simulations using the voxel method. [Background technology]

[0002] The voxel method is a representative shape representation for shape simulations used to analyze dry etching processes. In the voxel method, a three-dimensional space is divided into three-dimensional cells (voxels), and information about each material is assigned to each cell. Furthermore, ions are injected from the top of the material as part of the dry etching process, and the ion trajectories are calculated. When an ion reaches a voxel on the material surface, the value assigned to that voxel is updated based on the physicochemical reaction, thereby calculating the shape evolution. Shape simulations using the voxel method require fast and accurate simulation of dry etching processes for large and complex shapes. Generally, in shape simulations using the voxel method, reducing the voxel size (increasing the number of voxels) results in a more precise shape representation and improved calculation accuracy, but it also increases the calculation time. For example, Patent Document 1 proposes a simulation device that can adjust the voxel size according to the machining accuracy in order to reduce the calculation time required for simulation while improving display accuracy. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] International Publication No. 2023 / 062756 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] The objective of this invention is to provide a simulation device that performs high-speed and precise shape simulations using the voxel method.

Means for Solving the Problem

[0005] The gist of the present invention is as follows. (1) A simulation execution unit that performs shape simulation using voxels having a first size, and a conversion unit that converts the voxels on which the shape simulation has been performed into voxels having a second size smaller than the first size. A simulation device having the above.

[0006] (2) Before performing the shape simulation, the conversion unit converts voxels having a third size smaller than the first size into voxels having the first size. A simulation device.

[0007] (3) The conversion unit converts the voxels having the third size into the optimal voxels having the first size according to the shape of the input structure. The optimal first size is a voxel size that can decompose the smallest structure of the input shape and can decompose the narrowest gas region with at least 3 voxels. A simulation device.

[0008] (4) The second size and the third size are the same. A simulation device.

[0009] (5) The simulation execution unit uses the ratio of the third size to the first size as an input parameter. A simulation device.

[0010] (6) The conversion unit uses surface extraction to convert the voxels on which the shape simulation has been performed into voxels having the second size. A simulation device.

[0011] (7) The conversion unit is a simulation device that adjusts the number of incident ions and the number of reaction sites in the voxel so that the volume change in the shape simulation using the first size voxel matches the volume change in the shape simulation using the second size voxel.

[0012] (8) The conversion unit adjusts the collision position so that the collision position between the incident ion and the material when performing a shape simulation using the first size voxel is the same as the collision position between the incident ion and the material when performing a shape simulation using the second size voxel. Simulation device.

[0013] (9) The conversion unit is If one voxel having the first size has a thin film material, and another voxel having the first size has another thin film material, and neither the thin film material nor the other thin film material constitutes a single voxel, The voxel shape information relating to the thin film material and the other thin film material is stored in the storage unit. The thin film material and the other thin film material are combined and surface extraction is performed. After converting the voxels having the first size to voxels having the second size, the thin film material and the other thin film material are distributed to the voxels of the second size using the information. Simulation device. [Brief explanation of the drawing]

[0014] [Figure 1] This is a block diagram showing the configuration of the simulation device. [Figure 2] This is a flowchart showing the operation of the simulation device. [Figure 3] This is a diagram used to explain shape simulation. [Figure 4-1] This is a diagram to further explain the shape simulation. [Figure 4-2] This is a diagram to further explain the shape simulation. [Figure 5] This graph shows the relationship between simulation time and voxel size. [Figure 6a] This diagram illustrates the adjustment of collision positions in shape simulation. [Figure 6b] This diagram illustrates the adjustment of collision positions in shape simulation. [Figure 6c] This diagram illustrates the adjustment of collision positions in shape simulation. [Figure 6d] This diagram illustrates the adjustment of collision positions in shape simulation. [Figure 6e] This diagram illustrates the adjustment of collision positions in shape simulation. [Figure 6f] This diagram illustrates an example where collision position adjustments are not performed in shape simulation. [Figure 7] This diagram illustrates the distribution of thin film material in shape simulation. [Modes for carrying out the invention]

[0015] Figure 1 is a block diagram showing the configuration of the simulation device. The simulation device has a control unit and a memory unit. The control unit is a processor such as a CPU. It has a memory unit. The memory unit has a volatile memory such as RAM used as the processor's working memory, and a non-volatile memory such as ROM in which programs and data executed by the processor are stored. The simulation device is a computer such as a personal computer, and has an input unit, an output unit, a communication unit, etc. (not shown).

[0016] The control unit includes a simulation execution unit and a conversion unit. The simulation execution unit performs shape simulation using a first large-sized voxel. Due to the large size of the voxel, shape simulation can be performed at high speed. The conversion unit converts the voxels from which the shape simulation was performed into voxels having a second size smaller than the first size, in order to make the rough shape caused by the first size into a smooth shape. In this way, the present invention enables high-speed and precise shape simulation.

[0017] Figure 2 is a flowchart showing the operation of the simulation device, and Figure 3 is a diagram for explaining shape simulation. In step S1, the conversion unit, as a preprocessing step, divides the input structure into voxels having a third size smaller than the first size, for example, according to the shape of the input structure (see Figure 3(a)). In Figure 3, the white areas represent voxels in the gas region without material, the shaded areas represent voxels of the first material (e.g., nitride film), and the dark gray areas represent voxels of the second material (e.g., substrate). In step S2, before performing the shape simulation, the transformation unit transforms fine voxels of a third size into coarse voxels of a first size according to the shape of the input structure (see Figure 3(b)). The optimal first size is a voxel size that can resolve the smallest structure of the input shape and resolve the narrowest gas region with at least 3 voxels. In step S3, the simulation execution unit performs a shape simulation using coarse voxels (see Figure 3(c)). Specifically, it calculates the ion flux and trajectory using coarse voxels, and calculates the surface reaction and shape propagation. Here, the simulation execution unit may use the ratio of the third size to the first size as an input parameter. In step S4, the conversion unit performs surface extraction on the rough voxels (see Figure 3(d)). When the conversion unit performs surface extraction on the boundaries between the white voxels without material and the diagonal voxels of the first material, and the boundaries between the diagonal voxels of the first material and the dark gray voxels of the second material, smooth material boundaries are obtained, as shown in Figure 3(d). In step S5, the transformation unit converts the coarse voxels obtained from the shape simulation into fine voxels having a second size (see Figure 3(e)). Note that the second and third sizes may be the same or different.

[0018] The first size (the length of one side of a voxel) should ideally be large enough to cover the smallest initial shape of the shape simulation with at least a few voxels. This is because voxels smaller than this size cannot accurately represent particle collision detection or the relative positions of materials.

[0019] Figure 4 is a diagram that further illustrates the shape simulation. Figure 4(a) is a cross-sectional view of the initial shape, in which oxide and nitride films are alternately stacked on the substrate, and photoresist is placed on top of them at 12 nm intervals. Next, an etching shape simulation using the voxel method is performed. The etching reaction considered is the etching reaction of oxide and nitride films by ions, and the photoresist is not etched. In this example, a voxel method is used in which multiple material types are assigned to one voxel, but in the present invention, a voxel method in which one material type is assigned to one voxel may also be used. Figure 4(b) shows the simulation results of the comparative example, in which shape simulation was performed with a voxel size of 1 nm. In the comparative example, etching was performed up to the fifth nitride film from the top, excluding the photoresist, and the material boundary was smooth. Figure 4(c) shows the simulation results obtained by performing a shape simulation with a 3 nm voxel size according to the present invention, and then converting it to a 1 nm voxel size without surface extraction. In this example of the present invention, etching is performed up to the fifth nitride film from the top, similar to the comparative example, but the material boundary is less clear than in the comparative example. This is because, since surface extraction is not used when converting from a 3 nm voxel size to a 1 nm voxel size, the etched voxels include both the gas region and the material. Figure 4(d) shows the simulation results obtained by performing a shape simulation with a 3 nm voxel size according to the present invention, and then converting it to a 1 nm voxel size using surface extraction. In surface extraction, the material surface was extracted using the marching cubes method as an isosurface of the material volume, and polygons were generated. In the present invention example, etching was performed up to the 5th nitride film from the top, similar to the comparative example, and the material boundary was as smooth as in the comparative example. Figure 4(e) shows the simulation results obtained by performing a shape simulation with a 5 nm voxel size according to the present invention, and then converting it to a 1 nm voxel size using surface extraction. In the example of the present invention, etching is only performed up to the fourth nitride film layer from the top, but the material boundary is as smooth as in the comparative example. The number of layers etched from the top depends on the spacing of the photoresist and the first size of the voxels used in the shape simulation. In this example, when the spacing of the photoresist is 12 nm, as shown in Figure 4(e), the depth to which etching is removed changes when using a 5 nm voxel size in the shape simulation. Thus, if the voxel size is too large, accurate simulation results cannot be obtained.

[0020] Figure 4(f) shows the voxel data for voxels 1 to 8 used in the shape simulation, corresponding to the positions shown in Figure 4(g). In this example, the voxel method is used, in which multiple material types are assigned to a single voxel. Voxels 1-4 contain 100% material A, voxel 5 contains 100% material B, voxel 6 contains 50% material B and 50% material C, and voxels 7 and 8 are in the gas region and therefore contain no material.

[0021] Figure 5 is a graph showing the relationship between simulation time and voxel size. In Figure 5, the vertical axis shows time (TAT: turnaround time), and the horizontal axis shows the cell size of the voxel divided by 1 nm. Data A is the data for the comparative example in Figure 4(b) where shape simulation was performed with a voxel size of 1 nm. Data B is data obtained by performing a shape simulation with a voxel size of 2 nm according to the present invention, and then converting it to a voxel size of 1 nm. Data C is the data shown in Figure 4(c), obtained by performing a shape simulation with a voxel size of 3 nm according to the present invention, and then converting it to a voxel size of 1 nm. As shown in Figure 5, increasing the voxel size significantly reduces the simulation time. Note that surface extraction was not used in this shape simulation. In many simulations, the shape simulation using the voxel method takes longer than the surface extraction time; therefore, to clearly demonstrate the time-saving effect of using coarser voxels, the calculation time for the shape simulation alone is shown in Figure 5.

[0022] Figures 6(a) to 6(e) are diagrams illustrating the adjustment of collision positions in shape simulation. In Figure 6(a), the voxel size is 1 nm, and in Figure 6(b), the voxel size is 3 nm. When considering ion emission from the same source position, in Figure 6(a), the incident ion collides with the material at position X, whereas in Figure 6(b), the incident ion collides with the material at position Y. Since high-precision simulation results cannot be obtained when the collision position between the incident ion and the material differs in this way, it is preferable that the conversion unit adjusts the collision position so that the collision position between the incident ion and the material when performing a shape simulation using coarse voxels with the first size shown in Figure 6(b) is the same as the collision position between the incident ion and the material when performing a shape simulation using fine voxels with the second size shown in Figure 6(a). Specifically, the conversion unit adjusts the collision position using the following algorithm.

[0023] Firstly, in the shape simulation shown in Figure 6(b), the conversion unit calculates the ion trajectory from the source position to the material surface of the voxel. The ion trajectory is determined from the position and velocity of the ions.

[0024] Secondly, in the shape simulation shown in Figure 6(b), the transformation unit calculates the total material volume of the voxel that the incident ion collides with and each of the surrounding voxels (typically, among ±3 to ±5 voxels in the xyz directions, voxels that have material in contact with the gas region). Figure 6(c) shows that in the xz plane, three voxels in the ±z direction, centered around the voxel V0 where the incident ion collided, are the voxels for which the material volume should be calculated. Figure 6(d) shows that in the yz plane, a total of 49 voxels, three in the ±z direction and three in the ±y direction, centered around the voxel V0 where the incident ion collided, are the voxels for which the material volume should be calculated.

[0025] Thirdly, the conversion unit extracts the material boundary (least squares plane) shown in Figure 6(e) from the calculated total material volume using the least squares method.

[0026] Fourth, the conversion unit calculates the intersection point (position X) between the ion trajectory and the material boundary, and sets this intersection point as the actual collision position. The material boundaries calculated from coarse voxels and those calculated from fine voxels are almost identical. Therefore, the collision position between incident ions and material in shape simulations using coarse voxels is the same as the collision position between incident ions and material in shape simulations using fine voxels. If no intersection points exist, the conversion unit determines that the ions are not colliding and continues calculating the ion trajectories.

[0027] Figure 6(f) illustrates an example where the collision position is not adjusted in the shape simulation. In this example, we will consider ion reflection. Ion reflection is defined as the reaction in which a colliding ion is reflected off the material surface, similar to elastic scattering. Specifically, the reflection algorithm when the collision position is not adjusted is as follows. First, identify the voxel V0 upon which the incident ion collides. Secondly, as described above, the least-squares plane of the material surface and its normal vector Ny are calculated using the total material volume of voxel V0 and each surrounding voxel. The position Z and its normal vector Nz are used to calculate the normal vector Ny of the material surface. Thirdly, assuming that the incident ion is reflected from the surface of voxel V0, the normal vector We determine the angle α between Ny and the trajectory of the incident ion. Since the incident ion is reflected at the same angle α, we calculate the trajectory of this reflected ion (dashed arrow in the figure). In this example, the material surface extends in the vertical direction (z-direction), so the normal vectors Ny and Nz extend in the horizontal direction (x-direction). However, in actual shapes, the material surface may extend diagonally, so it is necessary to correctly calculate the normal vectors to determine the reflection direction.

[0028] Figure 7 is a diagram illustrating the distribution of thin film material in shape simulation. Oxide and nitride films are alternately layered on a substrate, and a photoresist is placed on top of them. As shown in the enlarged view (a1) of Figure 7(a), a first voxel having a first size comprises a nitride film material n and a first thin film material m1, and as shown in the enlarged view (a2), another second voxel having a first size comprises an oxide film material o and a second thin film material m2. The photoresist, nitride film material, oxide film material, and substrate material each constitute one voxel individually, whereas the first thin film material m1 and the second thin film material m2 do not each constitute one voxel individually in all voxels, including the first and second voxels. Thus, in the case of thin film materials with a volume less than one voxel, the surface cannot be directly extracted when extracting the material surface from the isosurface of the material volume during surface extraction. Therefore, it is preferable to extract the boundaries of the thin film using the following algorithm.

[0029] Firstly, the conversion unit stores information about the voxel shapes of the first thin film material and the second thin film material in the storage unit. Secondly, as shown in Figure 7(b), the conversion unit treats the first thin film material and the second thin film material as a single material without distinction and performs surface extraction on them together. Specifically, as shown in Figure 7(c), the conversion unit determines, as isosurfaces of the surface extraction, a material boundary B1 determined from the isosurfaces of all material volumes including the first thin film material and the second thin film material, and a material boundary B2 determined from the isosurfaces of all material volumes not including the first thin film material and the second thin film material. In this example, two thin film materials are combined into one, but there may be three or more thin film materials. Thirdly, as shown in Figure 7(d), the conversion unit uses material boundaries B1 and B2 to convert coarse voxels of a first size into fine voxels of a second size, and then recovers the thin film volume from the difference between B1 and B2. Fifth, as shown in Figure 7(e), the conversion unit reads voxel shape information relating to the first thin film material and the second thin film material from the storage unit, and uses this information to distribute the first thin film material and the second thin film material to voxels having a second size.

[0030] The conversion unit preferably adjusts the number of incident ions and the number of reaction sites in the voxel so that the volume change amount of the shape simulation using voxels having a first size matches the volume change amount of the shape simulation using voxels having a second size.

[0031] Hereinafter, a method of changing the number of ion particles, the number of individual particles in the voxel, and the number of its reaction sites when changing the voxel size will be described. In the voxel considered here, the individual particles in one voxel are divided into reaction sites and non-reaction sites, and it is assumed that the incident ions can react only with the particles in the reaction sites. When the number of particles in the reaction sites decreases due to the reaction with ions, the particles in the non-reaction sites are re-registered as reaction sites.

[0032] Hereinafter, a method of changing the number of ion particles according to the voxel size will be described. Here, a voxel method in which multiple material particles 1 / d are present in one voxel will be considered. Let the voxel size be a [nm] and Avogadro's number be N a , and the silicon volume per mole be V si . Then, the number of silicon atoms (particles) N realvoxel present in one voxel is N realvoxel = N a ·a 3 / V si given by. In the simulation, since 1 / d particles are present in one voxel, the number of simulation silicon particles N simvoxel present in one voxel is N simvoxel = 1 / d becomes. The ratio of this N simvoxel to N realvoxel represents the ratio of the number of simulation silicon particles to the number of actual silicon particles, and since the ratio of the number of simulation gas particles N simgas to the number of actual gas particles N realgas is also the same ratio, N simvoxel / Nrealvoxel =N simgas / N realgas Therefore, the number of simulated gas particles N simgas teeth, N simgas =N realgas × (N simvoxel / N realvoxel )∝1 / (a 3 ·d) This is the result. Thus, the number of simulated gas particles N simgas Since this decreases as the voxel size increases, shape simulations using coarse voxels can be performed at high speed. To simulate actual shape evolution with different voxel sizes, the number of real particles whose shape changes per unit real time (ΔN) is required. realvoxel / Δt real ) is the number of particles whose shape changes per unit simulation time (ΔN simvoxel / Δt sim ) must be equal to the following: That is, the following must hold. ΔN realvoxel / Δt real =ΔN simvoxel / Δt sim Since the ratio of the etching process time to the actual number of ion particles is equal to the ratio of the simulation time to the simulated number of ion particles, by making the number of simulated ion particles dependent on the voxel size using the method described above, the number of particles whose shape changes per unit simulation time matches the number of actual particles whose shape changes per unit real time, and results that do not depend heavily on the voxel size can be obtained.

[0033] Next, we will explain how to change the number of particles at the reaction site according to the voxel size. As mentioned above, the number of simulated reaction particles N simsite and the actual number of particles N at the reaction site realsite The ratio is the number of simulated gas particles N simgas and the actual number of gas particles N realgas Since this is the same as the ratio, N simsite / N realsite =N simgas / N realgas This can be obtained. Furthermore, in the simulation, if the xy area is A, then the number of surface voxels is N. sim_surfacevoxel teeth, N sim_surfacevoxel =A / a 2 Therefore, the number of simulated reaction sites per voxel is n. simsite The voxel size dependency is n simsite =N simsite / N sim_surfacevoxel ∝ 1 / a This is the result. Typically, 50 particles are assigned to a 1 nm voxel based on the number of atoms in a silicon crystal, and 50 particles are assigned to the reaction sites. 2 / 3 If approximately 14 voxels are used, it is preferable to change the number of particles within the voxel and the number of particles at the reaction site, as shown in Table 1, when changing the size of the voxel.

[0034] [Table 1]

Claims

1. A simulation execution unit that performs shape simulation using voxels having a first size, A conversion unit that converts voxels obtained by performing a shape simulation into voxels having a second size smaller than the first size, A simulation device having the following features.

2. Before performing the shape simulation, the conversion unit converts a voxel having a third size smaller than the first size into a voxel having the first size. The simulation apparatus according to claim 1.

3. The conversion unit converts the voxels having the third size to voxels having the optimal first size according to the shape of the input structure. The optimal first size is a voxel size that can resolve the smallest structure of the input shape and resolve the narrowest gas region with at least three voxels. The simulation apparatus according to claim 2.

4. The second size and the third size are identical. The simulation apparatus according to claim 2.

5. The simulation execution unit uses the ratio of the third size to the first size as an input parameter. The simulation apparatus according to claim 2.

6. The conversion unit converts the voxels obtained by performing a shape simulation using surface extraction into voxels having the second size. The simulation apparatus according to claim 1.

7. The conversion unit adjusts the number of incident ions and the number of reaction sites within the voxel so that the volume change in the shape simulation using the first size voxel matches the volume change in the shape simulation using the second size voxel. The simulation apparatus according to claim 1.

8. The conversion unit adjusts the collision position so that the collision position between the incident ion and the material when performing a shape simulation using the first size voxel is the same as the collision position between the incident ion and the material when performing a shape simulation using the second size voxel. The simulation apparatus according to claim 1.

9. The conversion unit is If one voxel having the first size has a thin film material, and another voxel having the first size has another thin film material, and the thin film material and the other thin film material do not each constitute a single voxel, The voxel shape information relating to the thin film material and the other thin film material is stored in the storage unit. The thin film material and the other thin film material are combined and surface extraction is performed. After converting the voxels having the first size to voxels having the second size, the thin film material and the other thin film material are distributed to the voxels of the second size using the information. The simulation apparatus according to claim 1.

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