Shape simulation method

Abstract

This invention provides a shape simulation method that enables high-speed execution of shape simulations. [Solution] The method comprises a Voxel generation step of generating a Voxel in which the number of non-reactive simulated solid particles, the number of reactive simulated solid particles, and the type of bonding are set as parameters of a Voxel variable corresponding to a plurality of simulated solid particles; a gas particle setting step of setting initial conditions for gas particles; a particle transport calculation step of identifying the arrival position of gas particles; a surface reaction determination step of identifying the Voxel present at the arrival position of the gas particles and determining the surface reaction between the Voxel and the gas particles; a surface reaction calculation step of calculating the number of reactive particles and the bonding state in the parameters of the Voxel variable based on the change in bonding state for the determined surface reaction; and an update step of updating the parameters of the Voxel variable according to the calculation results.

Description

[Technical Field]

[0001] The present invention relates to a shape simulation method, and more particularly to a shape simulation method used in semiconductor manufacturing processes. [Background technology]

[0002] Conventionally, it has been known that Voxel-type shape simulation methods, which can take into account complex surface reactions, are used to develop highly complex semiconductor processing processes. In Voxel-type shape simulation methods, simulated solid particles are used to simulate the atoms and molecules within the actual solid crystal being processed. The shape of the object being processed can be simulated by a Voxel containing these simulated solid particles.

[0003] Voxel-based shape simulation methods include assigning one simulation solid particle to each voxel, and assigning multiple simulation solid particles to each voxel.

[0004] For example, the method described in Patent Document 1 represents the surface of the workpiece using multiple voxels and performs flux calculations at the centroid position of the voxels. This method assigns one simulated solid particle to each voxel. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2014-96400 [Patent Document 2] U.S. Patent No. 10599789 [Overview of the Initiative] [Problems that the invention aims to solve]

[0006] However, in the method of assigning one simulation solid particle to one voxel, the number of voxels used in the simulation is considered to be larger than that in the method of assigning a plurality of simulation solid particles to one voxel, so the amount of calculation also increases.

[0007] On the other hand, Patent Document 2 discloses a method of performing a shape simulation by assigning a plurality of simulation solid particles to one voxel by using a value representing the amount of substance in a three-dimensional region corresponding to the voxel.

[0008] However, the bonding state of the substance contained in the three-dimensional region corresponding to each voxel has not been simulated. For this reason, it is considered that the method of Patent Document 2 cannot accurately simulate a phenomenon in which the same type of solid particles, such as an atomic layer deposition process (ALD: Atomic Layer Deposition), can take a plurality of bonding states.

[0009] The present invention has been made in view of the above-described problems, and for example, a shape simulation method capable of executing a shape simulation in a semiconductor manufacturing process including an atomic layer deposition process or an atomic layer etching process on a substrate at high speed by accurately realizing it with a smaller number of voxels than in the conventional method.

Means for Solving the Problems

[0010] A simulation method according to a representative embodiment of the present invention is characterized by comprising: a Voxel generation step in which a Voxel is generated to which a plurality of simulation solid particles corresponding to the shape of a substrate to be simulated are assigned, and for each type of constituent material of the substrate to be simulated, the number of non-reactive simulation solid particles, the number of reactive simulation solid particles, and the type of bonding are set as parameters of a Voxel variable corresponding to the plurality of simulation solid particles; a gas particle setting step in which initial conditions for gas particles used in each step of a semiconductor manufacturing process are set; a particle transport calculation step in which particle transport of the gas particles in any of the steps is calculated from the initial conditions for the gas particles set in the gas particle setting step and the destination position of the gas particles is identified; a surface reaction determination step in which the Voxel located at the destination position of the gas particles identified in the particle transport calculation step is identified and the surface reaction between the Voxel and the gas particles is determined; a surface reaction calculation step in which the number of reactive simulation solid particles and the bonding state in the parameters of the Voxel variable are calculated based on the change in the bonding state for the determined surface reaction; and an update step in which the parameters of the Voxel variable are updated according to the results of the calculation. [Effects of the Invention]

[0011] According to the simulation method of the present invention, it is possible to accurately simulate the state of solid particles while performing shape simulation with fewer voxels compared to conventional methods, thereby enabling high-speed execution. [Brief explanation of the drawing]

[0012] [Figure 1] This figure shows an example of an atomic layer deposition process simulated by the shape simulation system of this embodiment. [Figure 2] Figure 1 shows an example of the shape at the start of the atomic layer deposition process. [Figure 3] Figure 1 shows an example of the shape at the end of the atomic layer deposition process. [Figure 4] This figure shows an example configuration of the shape simulation system of this embodiment. [Figure 5] This is a functional block diagram showing an example of a calculation unit in the shape simulation system of this embodiment. [Figure 6] This figure shows an example of the processing flow in the shape simulation method of this embodiment. [Figure 7] This figure shows the Voxel used in the shape simulation method of this embodiment. [Figure 8] This diagram illustrates the parameters set for Voxel variables. [Figure 9] This figure shows examples of parameters set for Voxel variables when the types of simulated solid particles are A, B, and C. [Figure 10] This figure shows the flux and process time for each type of gas supplied in each step of the atomic layer deposition process performed in the shape simulation of this embodiment. [Figure 11] This diagram shows the reactions that occur on a solid surface and their probabilities. [Figure 12] This figure shows a more detailed processing flow for determining the surface reaction in step S106. [Modes for carrying out the invention]

[0013] 1. Overview of the Embodiment First, a general overview of a typical embodiment of the invention disclosed in this application will be provided. In the following description, as an example, reference numerals on the drawings corresponding to the components of the invention are indicated in parentheses.

[0014] [1] A shape simulation method according to a representative embodiment of the present invention is a Voxel to which a plurality of simulation solid particles corresponding to the shape of a substrate to be simulated are assigned, and the Voxel is generated in which the number of non-reactive simulation solid particles, the number of reactive simulation solid particles, and the type of bonding are set as parameters of a Voxel variable corresponding to the plurality of simulation solid particles for each type of constituent material of the substrate to be simulated; a gas particle setting step is to set initial conditions for gas particles used in each step of a semiconductor manufacturing process; a particle transport calculation step is to calculate the particle transport of the gas particles in any of the steps from the initial conditions for the gas particles set in the gas particle setting step and identify the destination position of the gas particles; a surface reaction determination step is to identify the Voxel located at the destination position of the gas particles identified in the particle transport calculation step and determine the surface reaction between the Voxel and the gas particles; a surface reaction calculation step is to calculate the number of reactive simulation solid particles and the bonding state in the parameters of the Voxel variable based on the change in the bonding state for the determined surface reaction; and an update step is to update the parameters of the Voxel variable according to the results of the calculation.

[0015] [2] In the shape simulation method described in [1] above, the number of types of bonded reactive simulation solid particles set as a parameter of the Voxel variable may be the value obtained by raising the maximum number of simulation solid particles contained in 1 Voxel to the power of 1 / 3.

[0016] [3] In the shape simulation method described in [1] above, the number of reactable simulation solid particles set as a parameter of the Voxel variable may be the value obtained by raising the maximum number of simulation solid particles contained in 1 Voxel to the power of 2 / 3.

[0017] [4] In the shape simulation method described in [1] above, the maximum sum of the number of non-reactive simulation solid particles and the number of reactive simulation solid particles set as parameters of the Voxel variable may be divided by the Voxel volume, and the value obtained is equal to the atomic density of silicon in the substrate being simulated.

[0018] [5] In the shape simulation method described in [1] above, the parameters that can be set as the type of bonding of the reactive particles may include a first bond which is a reaction site that can be sputtered in the purging step of the atomic layer deposition process and a second bond which is a reaction site that cannot be sputtered.

[0019] [6] In the shape simulation method described in [1] above, at least one of the final result and the transition of the parameters set as Voxel variables may be output.

[0020] [7] A shape simulation program according to a typical embodiment of the present invention is a program that causes a computer to execute each step of the shape simulation method described in any of [1] to [6] above.

[0021] [8] A shape simulation system according to a typical embodiment of the present invention is a shape simulation system comprising a computing device and a storage device, wherein the storage device is a Voxel to which a plurality of simulation solid particles corresponding to the shape of a substrate to be simulated are assigned to the computing device, and a Voxel generation step is generated in which the number of non-reactive simulation solid particles, the number of reactive simulation solid particles and the bonding type are set as parameters of Voxel variables corresponding to the plurality of simulation solid particles for each type of constituent material of the substrate to be simulated, a gas particle setting step is set in which the initial conditions of gas particles used in each step of the semiconductor manufacturing process are set in the gas particle setting step A shape simulation system that stores a program that causes the system to execute: a particle transport calculation step that calculates the particle transport of the gas particles in any of the steps from the initial conditions of the gas particles set in the top and identifies the destination position of the gas particles; a surface reaction determination step that identifies the Voxel present at the destination position of the gas particles identified in the particle transport calculation step and determines the surface reaction between the Voxel and the gas particles; a surface reaction calculation step that calculates the number of reactable simulated solid particles and the bonding state in the parameters of the Voxel variable based on the change in the bonding state for the determined surface reaction; and an update step that updates the parameters of the Voxel variable according to the results of the calculation.

[0022] 2. Specific Examples of Embodiments Specific examples of embodiments of the present invention will be described below with reference to the drawings. In the following description, components common to each embodiment will be denoted by the same reference numerals, and repeated explanations will be omitted. It should also be noted that the drawings are schematic, and the dimensional relationships and ratios of each element may differ from reality. There may also be parts where the dimensional relationships and ratios differ between drawings.

[0023] First, the process simulated by the shape simulation system of this embodiment will be described. In this embodiment, the example of realizing shape simulation in a semiconductor manufacturing process using atomic layer deposition (ALD) will be used.

[0024] Figure 1 shows an example of an atomic layer deposition process simulated by the shape simulation system of this embodiment. Figure 2 shows an example of the shape at the start of the atomic layer deposition process in Figure 1, and Figure 3 shows an example of the shape at the end of the atomic layer deposition process in Figure 1.

[0025] Atomic layer deposition (ADD) is a film deposition process that utilizes self-limiting properties by applying multiple types of gaseous materials to the substrate surface. It is used in various semiconductor mass production processes, including gate oxide films, silicon nitride (SiNx) films, and metal wiring. ADD is a process that deposits films on a substrate by repeating multiple cycles of four steps, each involving the introduction of gaseous materials onto the substrate. The type of gas used in each step is different, and the effect of the gas on the substrate differs at each stage.

[0026] In Figure 1, (a) is the surface state at the start of the atomic layer deposition process, (b) is the surface state during the adsorption step (first step) of the atomic layer deposition process in which a first gas is introduced onto the substrate, (c) is the surface state during the first purging step (second step) of the atomic layer deposition process in which a second gas is introduced onto the substrate, (d) is the surface state during the activation step (third step) of the atomic layer deposition process in which a third gas is introduced onto the substrate, and (e) is the surface state during the second purging step (fourth step) of the atomic layer deposition process in which a fourth gas is introduced onto the substrate. Thus, in the atomic layer deposition process, the four steps shown in (b) to (e) in Figure 1 are performed in one cycle, and this cycle is repeated multiple times until a film is finally formed.

[0027] First, as shown in Figure 1(b), in the adsorption process, a first gas is introduced, which is a precursor substance in the gaseous phase that reacts with the material constituting the substrate. As a result of the introduction of the first gas, the surface of the substrate can react with the precursor substance and change to either a chemiadsorption or physiadsorption state.

[0028] Next, as shown in Figure 1(c), in the first purging step, a second gas, which does not react with the substrate, is introduced to purge the gas used in the adsorption step. As a result of introducing the second gas, the first gas is purged, and the surface in the physicoad state can be sputtered.

[0029] Furthermore, as shown in Figure 1(d), unlike the adsorption process, a third gas, which is used for film formation, is introduced during the activation process. As a result of introducing the third gas, the material to be formed can be deposited on the surface of the substrate.

[0030] Subsequently, as shown in Figure 1(e), in the second purging step, the gas used in the activation step is purged by introducing a fourth gas, which does not react with the substrate. The gases used in each of the above steps of the atomic layer deposition process are selected according to the material of the substrate to be deposited and the material of the film to be formed.

[0031] In this embodiment of the shape simulation method, the shape of the substrate is simulated using Voxel, the behavior of the gas used is calculated, and the reaction between the gas and the substrate is identified. By calculating the changes caused by the identified reaction, the changing shape is identified, and shape simulation is realized. As a result, a substrate with the shape of Figure 3 is obtained by depositing a desired layer onto a substrate with the shape of Figure 2. As shown in Figure 3, according to this embodiment of the shape simulation method, it is possible to simulate the formation of a desired layer on the surface of a substrate with the shape of Figure 2.

[0032] Here, we will describe a shape simulation system that performs each process of the shape simulation method of this embodiment.

[0033] Figure 4 shows an example of the configuration of the shape simulation system according to this embodiment.

[0034] As shown in Figure 4, the shape simulation system of this embodiment can consist of a display device 100 such as a monitor 101, input devices 300 such as a keyboard 301, a mouse 302, a tablet 303, and a computing device 210 such as a computer 200 and a storage device 280. The computer 200 has an input unit for receiving data from the input device 300 and an output unit for outputting data to the display device 100, etc.

[0035] Figure 5 is a functional block diagram showing an example of a computing device in the shape simulation system of this embodiment.

[0036] The arithmetic unit 210 is composed of processors such as a CPU (Central Processing Unit) and a DSP (Digital Signal Processor). The storage device 280 has a storage area for storing programs that cause the arithmetic unit 210 to perform various data processing operations, and data such as parameters and calculation results used in the data processing by the arithmetic unit 210, and is composed of, for example, ROM (Read Only Memory), RAM (Random Access Memory), HDD, and flash memory.

[0037] Here, the program includes a shape simulation program that causes the computer (processor, memory, etc.) to function as each functional unit related to the shape simulation system, and is pre-installed, for example, on the storage device 280. The program can be configured as a computer-readable recording medium, i.e., a computer program product.

[0038] The shape simulation system 1 has the following functional units: an initial shape reading unit 211, a voxel generation unit 212, a voxel variable initialization unit 213, a gas particle initialization unit 214, a particle transport calculation unit 215, a surface reaction determination unit 216, a surface reaction calculation unit 217, a voxel gas particle update unit 218, a shape data conversion unit 219, and a shape data output unit 220. The shape simulation system 1 realizes the configuration of each functional unit shown in Figure 2 by having a processor perform various calculations according to a program stored in a memory or other storage device (not shown) and control peripheral circuits such as an A / D conversion circuit and an input / output I / F circuit.

[0039] Next, we will describe the shape simulation method performed by the shape simulation system described above.

[0040] Figure 6 shows an example of the processing flow in the shape simulation method of this embodiment.

[0041] In the shape simulation method of this embodiment, the initial shape reading unit 211 first reads data to be used as the initial shape (step S101). This shape data can be any data that represents the three-dimensional shape of the substrate to be simulated, and can be in any format such as Polygon or Voxel. The shape data may be pre-stored in the storage device 280 and received by the arithmetic unit 210, or it may be generated by the arithmetic unit 210 based on input from the input device 300, or it may be data received by the arithmetic unit 210 from an external data source via a network (not shown). The means for reading the shape data is not particularly limited.

[0042] In the shape simulation method of this embodiment, the materials constituting the substrate to be simulated and the gases used can be those used in conventional atomic layer deposition processes. Although the surface material formed will differ depending on the combination of substrate materials and gases, the process can be explained using similar steps, so specific material names will be omitted in the following explanation.

[0043] Next, the Voxel generation unit 212 generates shape data in Voxel format based on the shape read in step S101 (step S102). In step S101, a Voxel is generated that contains multiple simulation solid particles corresponding to the shape of the simulation target.

[0044] Figure 7 shows the Voxel used in the shape simulation method of this embodiment. The Voxel used in the shape simulation method of this embodiment will now be explained.

[0045] As shown in Figure 7, the Voxel used in the shape simulation method of this embodiment has multiple simulation solid particles within a single Voxel. Each simulation solid particle may correspond one-to-one with actual atoms and molecules to correspond to the density of actual atoms and molecules constituting the substrate being simulated, or multiple actual atoms and molecules may be associated with a single simulation solid particle. In either case, the external shape of the simulation solid particles contained within the Voxel corresponds to the shape of the target being simulated. The simulation solid particles are identified as different types of particles depending on the type of actual atoms and molecules they correspond to.

[0046] The shape data of the voxels generated by the voxel generation unit 212 can be displayed on the display device 100 as, for example, the shape shown in Figure 2. In Figure 2, the arrows indicate the gas path introduced into the substrate for illustrative purposes and do not need to be displayed on the display device 100.

[0047] Next, the Voxel variable initialization unit 213 performs the initialization of the Voxel variables (step S103). The Voxel generated in step S102 has Voxel variables. In the initialization of Voxel variables, the Voxel generated in step S102 is set with Voxel variables that represent the state of the simulated solid particles present within the Voxel as parameters.

[0048] In initializing the Voxel variables, specifically, for each type of simulated solid particle contained within a Voxel, the number of simulated solid particles that do not react with the gas used in the process, the number of reactable simulated solid particles, and the bonding type are set as parameters for the Voxel variables. By providing Voxel variables that allow setting parameters for each type of constituent material of the substrate being simulated, it is possible to calculate surface reactions defined by the combination of gas particles and solid materials. Furthermore, by setting information about the shape, such as the surface normal vector of each Voxel, as parameters for the Voxel variables, shape-dependent calculations can be performed efficiently. The total number of simulated solid particles contained within one Voxel is the sum of the number of simulated solid particles that do not react with the gas used in the process and the number of reactable simulated solid particles. In this embodiment, the case where the maximum value of the total number of simulated solid particles contained within one Voxel is 64 is used as an example for explanation.

[0049] Figure 8 is a diagram illustrating the parameters set for the Voxel variables. Figure 9 is a diagram showing examples of parameters set for the Voxel variables when the types of simulated solid particles are A, B, and C.

[0050] As shown in Figure 8, several types of parameters corresponding to the number of simulated solid particles in the Voxel and parameters related to the shape of the Voxel are set as Voxel variables. Specifically, n represents the number of reactive particles (reactive simulated solid particles) corresponding to the number of simulated solid particles in the Voxel. r n indicates the number of non-reactive particles (simulated solid particles that do not react). i And a parameter indicating the binding state of the reactive particles is set. In this embodiment, the parameter indicating the binding state of the reactive particles is, for example, n, which represents the number of simulated solid particles in the chemisorption state among the reactive particles. cn represents the number of simulated solid particles in a single physisorption state among the reactive particles. ps n represents the number of simulated solid particles in a double physisorption state among the reactive particles. pd n represents the number of simulated solid particles in a triple physisorption state among the reactive particles. pt Four types of parameters are set. Each parameter ranges from 0 to n. smax The value can be the maximum value of the simulated solid particles that can be contained within the voxel. The voxel is set as a parameter (n vector) which represents the normal vector of the voxel surface.

[0051] The physiosorption state represents reaction sites that can be sputtered during the purging process of the atomic layer deposition process, while the chemisorption state represents reaction sites that cannot be sputtered during the purging process of the atomic layer deposition process. These surface states represent changes in the surface state that occur during the atomic layer deposition process. In this embodiment, these surface states can be set as parameters for the bonding type of reactive particles by using parameters that indicate the bonding state. For example, reaction sites that can be sputtered during the purging process of the atomic layer deposition process can be set as physiosorption (first bonding), and reaction sites that cannot be sputtered during the purging process of the atomic layer deposition process can be set as chemisorption (second bonding). Therefore, by using parameters that identify these surface states, the shape simulation of the atomic layer deposition process can be performed at high speed.

[0052] The parameters shown in FIG. 8 may be limited to the following values. The number of types of bonding types of reactive simulation solid particles, which is a parameter indicating the bonding state of reactive particles, is the value obtained by taking the cube root of the maximum number of simulation solid particles included in 1 Voxel. When the value obtained by taking the cube root includes a decimal fraction, the value obtained by rounding up the decimal fraction to an integer is set as the number of types of bonding types of reactive simulation solid particles. In the present embodiment, since the maximum value of the total number of simulation solid particles included in 1 Voxel is 64, the number of types of parameters representing the bonding state is the cube root of 64 (64 1 / 3 = 4), and as described above, 4 types of n c , n ps , n pd , and n pt are set. As a result, accurate simulation can be performed with a small number of parameters. The more types of parameters there are, the more types of surface states can be supported, and the calculation accuracy is improved, but the calculation cost also increases. By setting the number of types of bonding types of reactive simulation solid particles in this way, an optimal value considering accuracy and cost can be set. It can be said that this setting is a condition under which each layer of a cube in which the bonding types of one layer are composed of a single bonding type can be composed of different layers.

[0053] In the present embodiment, the value of n r indicating the number of reactive simulation solid particles is the value obtained by taking the 2 / 3 power of the maximum number of simulation solid particles included in 1 Voxel. When the value obtained by taking the 2 / 3 power includes a decimal fraction, the value obtained by rounding up the decimal fraction to an integer is set as the number of reactive simulation solid particles. As a result, the number of reactive particles in the Voxel becomes equal to the number of particles in one plane when all the particles are assembled in a cubic shape, and the reactive particles can be made to correspond to the surface reaction sites, so that accurate simulation can be performed. For example, in the case of the present embodiment, since the maximum value of the total number of simulation solid particles included in 1 Voxel is 64, the value obtained by taking the 2 / 3 power of 64 (64 2 / 3 ) is 16.

[0054] In this embodiment, the number of simulated solid particles per voxel is shown (n r +n i The maximum value of ) divided by the Voxel volume is equal to the atomic density of silicon in the substrate being simulated. The atomic density of silicon is 50 atoms / nm 3 ]. In this case, it indicates the number of particles per voxel (n r +n i The value obtained by dividing the maximum value of ) by the Voxel volume is 50 [particles / nm] 3 The total number of simulated solid particles per voxel can be set to ]. This allows for accurate shape simulation of silicon devices.

[0055] As shown in Figure 9, when the types of solid particles are A, B, and C, six types of parameters are set for each type of simulated solid particle A, B, and C, corresponding to the simulated solid particles. Specifically, once the maximum number of reactive particles for each voxel is determined, the number of reactive particles for each type of substance is assigned according to the volume fraction value of each voxel, which is determined in accordance with the initial shape read in step S101. For example, if the maximum number of reactive particles is 16 and the types of constituent materials of the substrate to be simulated are substance A and substance B, the numbers can be assigned as follows according to the volume fractions of substances A and B. Specifically, if the volume fraction is 75% for substance A and 25% for substance B, the number of reactive particles can be set to A=12 and B=4; if the volume fraction is 50% for substance A and 50% for substance B, the number of reactive particles can be set to A=8 and B=8; and if the volume fraction is 25% for substance A and 75% for substance B, the number of reactive particles can be set to A=4 and B=12. The same method is used for assigning three or more types of substances, and if the division is not exact, the result is rounded to the nearest whole number.

[0056] In the shape simulation system of this embodiment, as shown in Figure 9, for each generated voxel, parameters indicating the number of non-reactive simulated solid particles, the number of reactive simulated solid particles, and the bonding type are set as voxel variables for each type of simulated solid particle contained within. The set voxel variable parameters shown in Figure 9 are stored in the storage device 280. With this configuration, the surface reaction described later can be calculated on a voxel-by-voxel basis.

[0057] Next, the gas particle initialization unit 214 performs the gas particle initialization process (step S104). In the gas particle initialization process in step S104, for each step of the atomic layer deposition process, the number of each type of gas particle and the initial conditions of the gas particles are determined randomly according to a distribution given based on the Monte-Carlo method, and assigned to each gas particle, thereby setting the initial state of the gas particles used in each step. The initial conditions include the initial position and initial velocity of the gas particles.

[0058] Figure 10 shows the flux and process time for each gas type supplied in each step of the atomic layer deposition process performed in the shape simulation of this embodiment. In this embodiment, the atomic layer deposition process is described using the case where the gas supply process shown in Figure 1 is performed 10 times as an example, but is not limited to this.

[0059] In step S104, the gas particles are initialized for the gas supplied in each gas supply process in all 10 cycles. In the shape simulation, the number of cycles in the gas supply process and the type and number of gases used in each gas supply process may be pre-set and stored in the memory device 280 so that they can be specified using the input device 300, or they may be input from the input device 300 at the timing up to step S104, or from an external source via the network.

[0060] In step S104, the number of simulated gas particles is adjusted to correspond to the number of actual gas particles and solid particles, and the number of simulated solid particles, in order to calculate the orbits of particles (Monte Carlo particles) generated by the Monte Carlo method in accordance with the actual gas particles and perform reaction calculations.

[0061] Specifically, the number of gas particles generated can be calculated from the actual number of gas particles, the actual number of solid particles, and the simulated number of solid particles.

[0062] Here, the actual number of gas particles supplied in each gas supply process is given by the gas flux F[mol]. 1 m -2 s -1 ] and process time t[s] and simulation domain A[m 2 ] and Avogadro's constant Na[mol -1 It can be calculated from ]. The number of gas particles generated is derived from the following equation (1).

[0063] The actual number of solid particles contained within the region corresponding to TIFF2026091638000002.tif141701Voxel is equal to the molar volume Vsi[m³] of the substrate. 3 mol -1 ] and Voxel cell size a 3 [m 3 ] and Avogadro's constant Na[mol -1 It can be calculated from ]. The number of gas particles generated is derived from the following equation (2).

[0064] The number of simulated solid particles contained within the Voxel in TIFF2026091638000003.tif151701 can be calculated from the density d of the simulated solid particles within the Voxel. The number of simulated solid particles is derived from the following equation (3).

[0065] Therefore, the actual number of gas particles is derived from equation (5), which is a rearrangement of equation (4) below.

[0066] TIFF2026091638000005.tif33170 The initial positions (px, py, pz) of the gas particles are px=γ1, py=γ2, pz=z top It can be expressed as follows: The initial velocities of the gas particles are given by vx=sinθcosφ, vy=sinθsinφ, and vz=-cosθ. If the filename is TIFF2026091638000006.tif25170, It can be expressed as TIFF2026091638000007.tif6170. In these equations representing the initial position and initial velocity, random numbers are set for γ1 to γ4, and z top By setting the maximum value of the simulation domain, the initial position and initial velocity of the gas particles can be determined.

[0067] Next, the particle transport calculation unit 215 performs particle transport calculations (step S105). In the particle transport calculations, at any stage of the atomic layer deposition process, the transport of gas particles within a voxel is calculated using the initial conditions of the gas particles initialized in step S104, and the voxels that collide with those gas particles are identified. Various ray tracing techniques can be used for this calculation.

[0068] In the particle transport calculation, the initial conditions set in step S104 as the initial position and initial velocity The transport of particles within a voxel is calculated using TIFF2026091638000008.tif6170. Various ray tracing techniques can be used for this calculation. For example, the 3D DDA (Digital Differential Analyzer) method can be applied. In this method, ray tracing can calculate rays that show the transport path of particles based on initial coordinates and initial velocity vectors. The position of the gas particles initialized in step S104 is updated using the ray tracing method, and when a solid is reached, the process proceeds to the next step.

[0069] Next, the surface reaction determination unit 216 performs a surface reaction determination process (step S106). In the surface reaction determination, for voxels in which one or more simulated solid particles capable of reacting with the gas particles that collide with the voxel are identified, the reactions occurring on the solid surface are identified.

[0070] In the shape simulation method of this embodiment, as already identified in step S104, the type of gas supplied in each step of one cycle of the atomic layer deposition process shown in Figure 1 is fixed. However, the type of reaction that occurs when the gas is supplied occurs probabilistically depending on the bonding state of the surface material.

[0071] Figure 11 shows the reactions that occur on a solid surface and their probabilities. In Figure 11, when gas particles are supplied at each step of the atomic layer deposition process to be simulated, the type of reaction that occurs, the type of gas supplied, the bonding state of the solid particles to which the gas is supplied (surface material), the bonding state of the solid particles after the reaction (formed material), and the reaction probability are shown. The values ​​in Figure 11 may be pre-set, with the reaction probabilities for each gas used in each step for the type of substrate material being simulated, stored in the memory device 280 and made available for specification using the input device 300, or they may be input from the input device 300 or the like at the timing up to step S106.

[0072] The reaction and the resulting materials are probabilistically determined by the surface material of the substrate being simulated and the type of gas acting on it. These values ​​can be pre-set as shown in Figure 11, depending on the actual reaction that occurs. In the surface reaction determination process in step S106, the reaction can be identified using the pre-set values ​​shown in Figure 11.

[0073] Figure 11a shows that there are five reaction probabilities for gas A supplied in the first step. When the material of the solid particles on the surface to which gas A is supplied is S, D, or E, a chemisorption reaction occurs with a probability of "0.3", resulting in the production of solid particles of material B that strongly bond to the surface. Furthermore, when the solid particles on the surface to which gas A is supplied are material B in a "chemisorption" (chemical adsorption) or "physisisorption" (physical adsorption) state, a physisisorption reaction occurs with a probability of "0.001", resulting in the production of solid particles of material B that weakly bond to the surface.

[0074] Figure 11b shows that there is only one reaction probability for the gas N supplied in the second step. It is shown that when the solid particles on the surface to which gas N is supplied are material B, which is weakly bonded to the surface generated by "Physisorption", Purge occurs with a probability of "1.0", and the solid particles of material B are removed. In other words, material B, which is strongly bonded to the surface, cannot be sputtered in the purging process of the atomic layer deposition process, while material B, which is weakly bonded to the surface, can be sputtered in the purging process of the atomic layer deposition process.

[0075] Figure 11c shows that there are two reaction probabilities for gas C supplied in the third step. When the solid particles on the surface to which gas C is supplied are material B in a "chemisorption" state, a deposition reaction occurs with a probability of "0.9", resulting in the solid particles changing from material "B" to "D". When the solid particles on the surface to which gas C is supplied are material B in a "physisisorption" state, a deposition reaction occurs with a probability of "0.1", resulting in the solid particles changing from material "B" to "E".

[0076] As described above, in each step of one cycle of the atomic layer deposition process, different reaction states occur depending on the surface state of the surface material of the substrate being simulated. As shown in Figure 11, a reaction probability is set for the surface material of the substrate present in the voxels that collide with the gas used. In this embodiment, the surface state of the surface material of the substrate being simulated is simulated by the parameters of the voxel variables as the bonding state of reactive particles corresponding to the type of simulated solid particles corresponding to the surface material of the substrate. In the surface reaction determination process in step S106, the type of reaction is determined according to these set probabilities.

[0077] Figure 12 shows a more detailed processing flow for the surface reaction determination in step S106.

[0078] In surface reaction determination, target particle selection is first performed by determining the surface material (type of simulated solid particle) to be subjected to surface reaction determination (step S601). In the particle transport calculation in step S105, target particle selection is performed based on the number of reactive particles nr in the Voxel identified as the colliding Voxel.

[0079] The selection of target particles is performed according to the number of reactive particles nr. If the number of reactive particles nr in the Voxel is zero for all but one type, then the surface material type with a non-zero number of reactive particles nr is selected. If there are multiple surface materials with a non-zero number of reactive particles nr, then for each type of simulation solid particle corresponding to the non-zero surface material, a parameter range from 0 to 1 is set without overlap. Then, a random number with a value between 0 and 1 is generated, and the simulation solid particle type whose parameter range corresponds to the value of the random number is selected as the target particle.

[0080] Next, it is determined whether the material of the selected target particle exists (step S602). If the target particle could not be selected in step S601, it is determined that the material does not exist.

[0081] In step S602, if it is determined that a substance is present (S602: YES), a reaction equation is selected (step S603). The reaction equation is selected according to the reaction probability for each generated material, which is set based on the type of gas particle and the surface material (type of simulated solid particle). For this selection, the pre-set reaction probabilities described in Figure 11 can be used. The reaction probabilities are determined by extracting records of reaction probabilities corresponding to the type of gas particle and the surface material (type of simulated solid particle) from Figure 11, setting parameter ranges from 0 to 1 that do not overlap according to the reaction probabilities, and then generating random numbers with values ​​from 0 to 1, and identifying the reaction type of the record for which the parameter range corresponding to the value of the random number is set as the reaction equation. When setting the parameter ranges, the reaction probability and the yield of the sputter reaction may be changed depending on the energy of the gas particle and the collision angle with the surface, and re-emission may be included in the parameter range.

[0082] Next, it is determined whether or not a reaction equation exists (step S604). If there is no pre-set reaction equation (reaction type) (step S604: NO), it is determined that the gas particle to be calculated has been re-emitted at the Voxel to be calculated (step S605), and the collision position is used as the initial position of the gas particle, and the particle transport calculation in step S105 is performed again according to random numbers in the cosine distribution. Similarly, if it is determined that there is no substance in step S602 (step S602: NO), the process proceeds to the re-emission process in step S605.

[0083] If the reaction equation resulting from the collision of gas particles in step S604 can be identified, proceed to step S107.

[0084] Next, the surface reaction calculation unit 217 performs a surface reaction calculation based on the surface reaction determined in step S106 (step S107). In the surface reaction calculation, the changes in the Voxel variables are identified by performing the surface reaction calculation based on the reaction equation determined in step S106. Among the reactive particles contained in the Voxel, the type of reactive particle is identified based on the reaction equation selected in step S106, and the surface reaction calculation is performed according to the state of the reactive particle (state of the variable).

[0085] The surface reaction calculation is a calculation in which the parameters of the Voxel variables are changed according to the surface reaction determined in step S106. For example, in the case of simulating an atomic layer deposition process in which there are four types of bonding species of reactable simulated solid particles, as in this embodiment, the surface reaction calculation identifies the changes in the Voxel variables according to the algorithms shown in (Condition 1) to (Condition 10) below. In the algorithms shown in (Condition 1) to (Condition 10) below, the n of the Voxel variables r From the value of n c The value and n ps The value and n pd The value and n pt The value obtained by subtracting the value of (n r -n c -n ps -n pd -n pt ) is "n_normal", and n c The value of n is "n_chemi", and n ps The value of n is "n_physi_single", and n pd The value of n is "n_physi_double", and n pt The value is "n_physi_triple".

[0086] Among the following algorithms, the parameter changes are identified according to the conditions corresponding to the parameters of the Voxel variables and the reaction type for the type of simulated solid particle corresponding to the target particle selected in step S106. (Condition 1) If chemisorption occurs when n_normal exists, decrease n_normal by 1 and increase n_chemi by 1. (Condition 2) If physisorption occurs when n_chemi exists, reduce n_chemi by one and increase n_physi_single. (Condition 3) If physisorption occurs while n_physi_single exists, reduce the number of n_physi_single by one and increase the number of n_physi_double by one. (Condition 4) If physisorption occurs while n_physi_double exists, reduce the number of n_physi_doubles by one and increase the number of n_physi_triples by one. (Condition 5) If only n_physi_triple or n_normal exist, physisorption will not occur. (Condition 6) If n_physi_triple exists, when purge occurs, reduce the number of n_physi_triple by one and increase the number of n_physi_double by one. (Condition 7) If n_physi_double exists, when a purge occurs, reduce n_physi_double by one and increase n_physi_single by one. (Condition 8) If n_physi_single exists, when purge occurs, reduce n_physi_single by one and increase n_chemi by one. (Condition 9) If only n_chemi or n_normal exists, no purge will occur. (Condition 10) If normal Adsorption occurs when there is an n_chemi, n_physi_single, n_physi_double, or n_physi_triple, decrease the number of n_chemi, n_physi_single, n_physi_double, or n_physi_triple by one and increase the number of n_normal by one.

[0087] Of the algorithms described above (Condition 1) to (Condition 10), (Condition 1) to (Condition 5) and (Condition 10) are algorithms for processing using gas particles supplied in the first step, and (Condition 6) to (Condition 9) are algorithms for processing using gas particles supplied in the second step.

[0088] In the shape simulation method of this embodiment, by introducing Voxel variables and processing them according to the algorithm described above, it is possible to calculate surface reactions according to the bonding state without defining the position and adjacency relationships of each particle within the Voxel and storing that data.

[0089] The algorithm described above simulates the constraints on changes in the bonding state depending on the adjacency relationships, so it can calculate surface reactions according to the bonding state without defining the position and adjacency relationships of each particle within the voxel and storing that data.

[0090] Next, the Voxel gas particle update unit 218 updates the Voxel variables based on the results of the surface reaction calculation in step S107, and if gas particles are generated as byproducts, it updates the variables by adding new gas particles (step S108). The Voxel gas particle update unit 218 may store the history of the updated Voxel variables in the memory device 280. This allows the shape simulation system 1 to output the changes in the parameters set for the Voxel variables as needed.

[0091] The Voxel gas particle renewal unit 218 repeats the processes from step S105 to step S108 for each step, for a number of gas particles determined from the process time and flux. After all the gas particles initialized in step S104, that is, after all the processes have been repeated 10 times, the Voxel gas particle renewal unit 218 calculates the shape evolution.

[0092] Once the shape evolution calculation is complete, the shape data conversion unit 219 converts the shape data into a data format that can be output from the Voxel data, if necessary (step S109).

[0093] The shape data output unit 220 outputs the final shape based on the data converted in step S109 (step S110). The shape of the Voxel output by the shape data output unit 220 can be displayed on the display device 100 as, for example, the shape shown in Figure 3.

[0094] <<Extension of the Embodiment>> Although the present inventors have described the invention in detail based on embodiments, it goes without saying that the present invention is not limited thereto and can be modified in various ways without departing from its essence.

[0095] This embodiment of the shape simulation system will be explained using the example of realizing shape simulation in an atomic layer deposition process, but it can be used to realize shape simulation in various semiconductor manufacturing processes. For example, it can also realize shape simulation in an atomic layer etching process. In that case, in the third step, instead of depositing a material to be formed on the surface of the substrate, the substrate is etched using a gas that etches the substrate. This embodiment of the shape simulation system can realize more accurate shape simulation of processes that include reactions in which the reaction probability differs depending on the bonding state with adjacent solid particles in various semiconductor manufacturing processes such as chemical vapor deposition (CVD), plasma CVD, reactive ion etching, and physical sputtering. In that case, Voxel variables corresponding to the bonding type are set, as in this embodiment, and surface reaction calculations corresponding to reactions dependent on the bonding type are performed.

[0096] The configuration of the shape simulation system in this embodiment is not limited to the configurations shown in Figures 4 and 5. For example, in the above embodiment, the arithmetic unit 210 was described as performing processing based on data stored in the storage device 280, but it is not limited to this. The arithmetic unit 210 can be configured to perform processing based on data received from an external data source via a network. The network communication method is not limited to wireless; it may also be configured as a wired connection. In that case, an Ethernet® router can be used instead of the wireless LAN base station 13.

[0097] In the embodiments described above, the surface reaction calculation algorithm explained in step S107 was described using an example where the algorithm for simulating an atomic layer deposition process with four types of bonding species in the reactable simulated solid particles identifies changes in the Voxel variables according to the algorithms shown in (Condition 1) to (Condition 10), but it is not limited to this. For example, if there are three or fewer types of bonding species, or if there are five or more types of bonding species, the atomic layer deposition simulation can be performed by imposing similar conditions on parameters that are increased or decreased. For example, if there are five types of bonding species, a new n pq By adding the parameter n_normal=n r -n c -n ps -n pd -n pt -n pqThe definition is redefined as follows: (Condition 4) is changed to "If physisorption occurs when n_physi_triple is present, decrease n_physi_triple by one and increase n_physi_quad by one"; (Condition 5) is changed to "If only n_physi_quad or n_normal is present, physisorption does not occur"; (Condition 6) is changed to "If purge occurs when n_physi_quad is present, decrease n_physi_quad by one and increase n_physi_triple by one"; (Condition 10) is changed to "If normal adsorption occurs when n_chemi or n_physi_single or n_physi_double or n_physi_triple or n_physi_quad is present, decrease n_chemi or n_physi_single or n_physi_double or n_physi_triple or n_physi_quad by one and increase n_normal by one". [Explanation of Symbols]

[0098] 1 Shape simulation system, 101 Monitor, 100 Display device, 200 Computer, 210 Calculation unit, 211 Initial shape reading unit, 212 Voxel generation unit, 213 Voxel variable initialization unit, 214 Gas particle initialization unit, 215 Particle transport calculation unit, 216 Surface reaction determination unit, 217 Surface reaction calculation unit, 218 Voxel gas particle update unit, 219 Shape data conversion unit, 220 Shape data output unit, 280 Storage device, 300 Input device, 301 Keyboard, 302 Mouse, 303 Tablet

Claims

1. A Voxel generation step that generates a Voxel to which multiple simulation solid particles corresponding to the shape of the substrate to be simulated are assigned, wherein for each type of constituent material of the substrate to be simulated, the number of non-reactive simulation solid particles, the number of reactive simulation solid particles, and the type of bonding are set as parameters of the Voxel variables corresponding to the multiple simulation solid particles, A gas particle setting step in which the initial conditions of the gas particles used in each step of the semiconductor manufacturing process are set, A particle transport calculation step involves calculating the particle transport of the gas particles in any of the steps from the initial conditions of the gas particles set in the gas particle setting step, and determining the destination position of the gas particles. A surface reaction determination step involves identifying the voxel located at the destination of the gas particle identified in the particle transport calculation step, and determining the surface reaction between the voxel and the gas particle. A surface reaction calculation step that calculates the number of reactable simulated solid particles and their bonding state in the parameters of the Voxel variable based on the change in bonding state for the determined surface reaction, An update step to update the parameters of the Voxel variable according to the results of the calculation, Equipped with, Shape simulation method.

2. In the shape simulation method described in claim 1, The number of types of bonded reactive simulation solid particles, set as a parameter of the aforementioned Voxel variable, is the value obtained by raising the maximum number of simulation solid particles contained in one Voxel to the power of 1 / 3. Shape simulation method.

3. In the shape simulation method described in claim 1, The number of reactable simulation solid particles set as a parameter of the Voxel variable is the value obtained by raising the maximum number of simulation solid particles contained in one Voxel to the power of 2 / 3. Shape simulation method.

4. In the shape simulation method described in claim 1, The value obtained by dividing the maximum sum of the number of non-reactive simulated solid particles and the number of reactive simulated solid particles, which is set as a parameter of the aforementioned Voxel variable, by the Voxel volume is equal to the atomic density of silicon in the substrate being simulated. Shape simulation method.

5. In the shape simulation method described in claim 1, The parameters that can be set as the type of bonding of the reactable particles include a first bond which is a reaction site that can be sputtered in the purging step of the atomic layer deposition process and a second bond which is a reaction site that cannot be sputtered. Shape simulation method.

6. In the shape simulation method described in claim 1, Output at least one of the final result and the transition of the parameter set as the Voxel variable. Shape simulation method.

7. A shape simulation program for causing a computer to perform each step of the shape simulation method described in any one of claims 1 to 6.

8. The computing unit and A shape simulation system comprising a memory device, The memory device is connected to the arithmetic unit, A Voxel generation step that generates a Voxel to which multiple simulation solid particles corresponding to the shape of the substrate to be simulated are assigned, wherein for each type of constituent material of the substrate to be simulated, the number of non-reactive simulation solid particles, the number of reactive simulation solid particles, and the type of bonding are set as parameters of the Voxel variables corresponding to the multiple simulation solid particles, A gas particle setting step in which the initial conditions of the gas particles used in each step of the semiconductor manufacturing process are set, A particle transport calculation step involves calculating the particle transport of the gas particles in any of the steps from the initial conditions of the gas particles set in the gas particle setting step, and determining the destination position of the gas particles. A surface reaction determination step involves identifying the voxel located at the destination of the gas particle identified in the particle transport calculation step, and determining the surface reaction between the voxel and the gas particle. A surface reaction calculation step that calculates the number of reactable simulated solid particles and their bonding state in the parameters of the Voxel variable based on the change in bonding state for the determined surface reaction, An update step to update the parameters of the Voxel variable according to the results of the calculation, The program that will be executed, which stores the program, Shape simulation system.

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