A method, device, terminal and storage medium for determining ion energy angle distribution

Abstract

A method, device, terminal and storage medium for determining ion energy angle distribution provided by the present invention belong to the technical field of chip manufacturing. The method includes: obtaining and establishing a fluid model based on the geometric parameters, background gas parameters and surface material parameters of a target capacitive coupling plasma chamber, solving the fluid model to obtain the spatio-temporal distribution of ionization rate and the spatio-temporal distribution of electromagnetic field; obtaining ion collision cross-section data; iteratively simulating the generation of ions, ion motion and the collision of ions and background gas molecules until the end condition is satisfied, so as to obtain the ion energy angle distribution of the ions reaching the substrate. The present invention generates new ions by using the ionization rate calculated by the fluid model, avoiding the simulation of the ionization process; uses the electromagnetic field calculated by the fluid model to drive particle motion, avoiding the calculation of charge density and the solution of electromagnetic field, and can solve the problem of repeated coupling of particles and fields, effectively reducing the time for determining the energy angle distribution of the ions reaching the substrate.

Description

Technical Field

[0001] The present invention relates to the technical field of chip manufacturing, and in particular to a method, device, terminal and storage medium for determining the ion energy angle distribution. Background Art

[0002] In the current field of high-precision chip manufacturing, ion-assisted etching has become the mainstream process. However, to achieve accurate simulation of ion-assisted etching, the key lies in obtaining the energy angle distribution of the ions participating in the etching. Currently, the industry generally uses the particle-in-cell method to determine the energy angle distribution of the ions participating in the etching. This method simulates the movement and collision process of macro-particles in the electromagnetic field, and then solves the Boltzmann equation. Finally, by statistically analyzing the energy and angle information of the ions reaching the substrate, the energy angle distribution is obtained. However, the particle-in-cell method needs to simulate the ionization process and perform frequent coupling calculations between the particles and the field. This step is not only complex and cumbersome, but also results in too long a calculation time for determining the energy angle distribution of the ions reaching the substrate.

[0003] Therefore, there are defects in the prior art and it needs to be improved and developed. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method, device, terminal and storage medium for determining the ion energy angle distribution in view of the above-mentioned defects of the prior art, aiming to solve the problem of too long time for determining the energy angle distribution of the ions reaching the substrate in the prior art.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] In the first aspect, an embodiment of the present invention provides a method for determining the ion energy angle distribution, the method comprising:

[0007] Obtain and, based on the geometric parameters, background gas parameters and surface material parameters of the target capacitively coupled plasma chamber, establish a fluid model using fluid simulation software, and solve the fluid model to obtain the spatio-temporal distribution of the ionization rate and the spatio-temporal distribution of the electromagnetic field;

[0008] Obtain ion collision cross-section data, where the ion collision cross-section data includes the collision cross-section values corresponding to various collision types between ions and background gas molecules;

[0009] Based on the spatio-temporal distribution of the electromagnetic field, the spatio-temporal distribution of the ionization rate, the ion collision cross-section data and the geometric parameters, iteratively simulate the generation of ions, ion movement and the collision between ions and background gas molecules in the target capacitively coupled plasma chamber until the end condition is met, to obtain the ion energy angle distribution of the ions reaching the substrate;

[0010] Among them, the spatio-temporal distribution of the ionization rate is used to reflect the rate at which background gas molecules in the target capacitively coupled plasma chamber are ionized to generate ions at different spatial positions and time points, and the spatio-temporal distribution of the electromagnetic field is used to reflect the changes in the electromagnetic field in the target capacitively coupled plasma chamber over time and space.

[0011] In one embodiment, solving the fluid model to obtain the spatio-temporal distribution of the ionization rate and the spatio-temporal distribution of the electromagnetic field includes:

[0012] Using the particle transport solver in the fluid simulation software to solve the fluid model to obtain the spatio-temporal distribution of the ionization rate;

[0013] Using the electromagnetic field solver in the fluid simulation software to solve the fluid model to obtain the spatio-temporal distribution of the electromagnetic field.

[0014] In one embodiment, based on the spatio-temporal distribution of the electromagnetic field, the spatio-temporal distribution of the ionization rate, the ion collision cross-section data, and the geometric parameters, iteratively simulate the generation of ions, ion motion, and the collision of ions and background gas molecules in the target capacitively coupled plasma chamber until the end condition is met, and obtain the ion energy-angle distribution of the ions reaching the substrate, including:

[0015] In each iteration, according to the spatio-temporal distribution of the ionization rate, simulate the generation of ions in the target capacitively coupled plasma chamber, and based on the spatio-temporal distribution of the electromagnetic field, the ion collision cross-section data, the geometric parameters, and the attribute information of each ion, simulate the ion motion and the collision of ions and background gas molecules in the target capacitively coupled plasma chamber;

[0016] When the end condition is met, stop the iteration, and based on the energy and angle of the ions reaching the substrate in the last iteration, obtain the ion energy-angle distribution of the ions reaching the substrate.

[0017] In one embodiment, according to the spatio-temporal distribution of the ionization rate, simulating the generation of ions in the target capacitively coupled plasma chamber includes:

[0018] According to the spatio-temporal distribution of the ionization rate, determine the ionization rate at the corresponding position in the target capacitively coupled plasma chamber at the current time step;

[0019] Accumulate the ionization rate at each corresponding position at the current time step and the ionization rate at the historical time step to obtain the ion generation progress corresponding to each corresponding position;

[0020] Compare the ion generation progress corresponding to each corresponding position with 1. If the ion generation progress at the corresponding position is equal to 1, simulate the generation of ions at the corresponding position.

[0021] In one embodiment, the geometric parameters include chamber boundary position data and substrate position data, and the attribute information includes mass, position, velocity, and charge; based on the electromagnetic field spatio-temporal distribution, the ion collision cross-section data, the geometric parameters, and the attribute information of each ion, simulating the ion motion and the collisions between ions and background gas molecules in the target capacitively coupled plasma chamber includes:

[0022] Obtaining the electromagnetic force on each ion based on the electromagnetic field spatio-temporal distribution and the charge of each ion;

[0023] Calculating and storing the position and velocity of each ion after simulated motion based on the mass, position, velocity, and the electromagnetic force on each ion;

[0024] Determining the position state of each ion based on the position of each ion after simulated motion, the chamber boundary position data, and the substrate position data, where the position state includes detaching from the target capacitively coupled plasma chamber boundary, arriving at the substrate, and being inside the target capacitively coupled plasma chamber and not arriving at the substrate;

[0025] Deleting the ions that have detached from the target capacitively coupled plasma chamber boundary, and recording the position and angle of the ions that have arrived at the substrate;

[0026] Using the Monte Carlo method to determine whether the ions located inside the target capacitively coupled plasma chamber and not arriving at the substrate collide with background gas molecules according to the ion collision cross-section data;

[0027] If a collision occurs, using the velocity of the ion after simulated collision and the position of the ion after simulated motion as the velocity and position of the ion for the next iteration;

[0028] If no collision occurs, using the velocity and position of the ion after simulated motion as the velocity and position of the ion for the next iteration.

[0029] In one embodiment, obtaining the electromagnetic force on each ion based on the electromagnetic field spatio-temporal distribution and the charge of each ion includes:

[0030] Calculating the electric field strength and magnetic field strength at the position of each ion by interpolation based on the electromagnetic field spatio-temporal distribution;

[0031] Obtaining the electromagnetic force on each ion based on the electric field strength, the magnetic field strength, and the charge of each ion.

[0032] In one embodiment, using the Monte Carlo method to determine whether the ions located inside the target capacitively coupled plasma chamber and not arriving at the substrate collide with background gas molecules according to the ion collision cross-section data includes:

[0033] Sum all the collision cross-section values in the ion collision cross-section data to obtain the total collision cross-section value;

[0034] Based on the total collision cross-section value, calculate the probability of each ion located in the target capacitively coupled plasma chamber and not reaching the substrate to have a collision currently;

[0035] Generate a first random number and compare it with the probability of each ion located in the target capacitively coupled plasma chamber and not reaching the substrate to have a collision currently, where the first random number is between 0 and 1;

[0036] If the first random number is less than the probability of this ion located in the target capacitively coupled plasma chamber and not reaching the substrate to have a collision currently, generate a second random number, determine the collision type of this ion based on the interval range where the second random number is located, and perform calculations based on the collision type to obtain the velocity of this ion after simulated collision;

[0037] If the first random number is greater than the probability of this ion to have a collision currently, maintain the velocity of this ion as the velocity after simulated ion movement.

[0038] In a second aspect, an ion energy angle distribution determination device according to an embodiment of the present invention further includes:

[0039] A fluid simulation module, configured to obtain and based on the geometric parameters, background gas parameters, and surface material parameters of the target capacitively coupled plasma chamber, establish a fluid model using fluid simulation software, solve the fluid model to obtain the spatio-temporal distribution of the ionization rate and the spatio-temporal distribution of the electromagnetic field, where the spatio-temporal distribution of the ionization rate is used to reflect the rate at which background gas molecules in the target capacitively coupled plasma chamber are ionized to generate ions at different spatial positions and time points, and the spatio-temporal distribution of the electromagnetic field is used to reflect the change of the electromagnetic field in the target capacitively coupled plasma chamber over time and space;

[0040] A data acquisition module, configured to acquire ion collision cross-section data, where the ion collision cross-section data includes collision cross-section values corresponding to various collision types between ions and background gas molecules;

[0041] A distribution determination module, configured to iteratively simulate the generation of ions, ion movement, and collisions between ions and background gas molecules in the target capacitively coupled plasma chamber based on the spatio-temporal distribution of the electromagnetic field, the spatio-temporal distribution of the ionization rate, the ion collision cross-section data, and the geometric parameters until an end condition is met, to obtain the ion energy angle distribution of the ions reaching the substrate.

[0042] Third aspect, an embodiment of the present invention further provides a terminal, where the terminal includes: a memory, a processor, and an ion energy angle distribution determination program stored on the memory and executable on the processor. When the ion energy angle distribution determination program is executed by the processor, it implements the steps of the ion energy angle distribution determination method as described above.

[0043] Fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium, where the computer-readable storage medium stores an ion energy angle distribution determination program, and the ion energy angle distribution determination program can be executed to implement the steps of the ion energy angle distribution determination method as described above.

[0044] Advantages of the present invention: Based on the geometric parameters, background gas parameters, and surface material parameters of the target capacitive coupling plasma chamber, the present invention uses fluid simulation software to establish a fluid model, solves the fluid model to obtain the spatio-temporal distribution of ionization rate and the spatio-temporal distribution of electromagnetic field; obtains ion collision cross-section data; iteratively simulates the generation of ions, ion movement, and the collision between ions and background gas molecules in the target capacitive coupling plasma chamber until the end condition is met, and obtains the ion energy angle distribution of the ions reaching the substrate. The present invention generates new ions using the ionization rate calculated by the fluid model, avoiding the simulation of the ionization process; the present invention uses the electromagnetic field calculated by the fluid model to drive particle movement, avoiding the calculation of charge density and the solution of electromagnetic field, and can solve the problem of repeated coupling between particles and fields, effectively reducing the time for determining the energy angle distribution of the ions reaching the substrate. Description of the Drawings

[0045] Figure 1 is a flowchart of a preferred embodiment of the ion energy angle distribution determination method in the present invention.

[0046] Figure 2 is a schematic diagram of data processing on CPU memory and GPU memory in the present invention.

[0047] Figure 3 is a comparison diagram of ion energy distributions obtained for the upper substrate by the particle-in-cell method and the method of the present invention.

[0048] Figure 4 is a comparison diagram of ion energy distributions obtained for the lower substrate by the particle-in-cell method and the method of the present invention.

[0049] Figure 5 is an ion angle distribution diagram obtained for the lower substrate by the particle-in-cell method.

[0050] Figure 6 is an ion angle distribution diagram obtained for the lower substrate by the method of the present invention.

[0051] Figure 7 It is a schematic structural diagram of a preferred embodiment of the ion energy angle distribution determination device in the present invention.

[0052] Figure 8 It is a block diagram of the terminal principle of the present invention. Specific embodiments

[0053] To make the objectives, technical solutions and advantages of the present invention clearer and more definite, the following further describes the present invention in detail with reference to the accompanying drawings and by way of examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0054] In the current high-precision chip manufacturing field, ion-assisted etching has become the mainstream process. However, to achieve accurate simulation of ion-assisted etching, the key lies in obtaining the energy angle distribution of the ions participating in the etching. Currently, the industry generally uses the particle-in-cell method to determine the energy angle distribution of the ions participating in the etching. This method simulates the movement and collision processes of macro particles in the electromagnetic field, and then solves the Boltzmann equation. Finally, by statistically analyzing the energy and angle information of the ions reaching the substrate, the energy angle distribution is obtained. However, the particle-in-cell method requires frequent coupling calculations of particles and fields. This step is not only complex and cumbersome, but also results in too long a time to determine the energy angle distribution of the ions reaching the substrate.

[0055] In view of the above-mentioned defects of the prior art, the present invention provides a method, device, terminal and storage medium for determining ion energy angle distribution. The method includes: based on the geometric parameters, background gas parameters and surface material parameters of a target capacitively coupled plasma chamber, establishing a fluid model using fluid simulation software, and solving the fluid model to obtain the spatio-temporal distribution of ionization rate and the spatio-temporal distribution of electromagnetic field; obtaining ion collision cross-section data; iteratively simulating the generation of ions, ion movement and the collision of ions and background gas molecules in the target capacitively coupled plasma chamber until the end condition is met, so as to obtain the ion energy angle distribution of the ions reaching the substrate. The present invention generates new ions using the ionization rate calculated by the fluid model, avoiding the simulation of the ionization process; the present invention uses the electromagnetic field calculated by the fluid model to drive the particle movement, avoiding the calculation of charge density and the solution of the electromagnetic field, and can solve the problem of repeated coupling of particles and fields, effectively reducing the time for determining the energy angle distribution of the ions reaching the substrate.

[0056] Please refer to Figure 1 , the method for determining ion energy angle distribution according to the embodiment of the present invention includes the following steps:

[0057] Step S100: Obtain the geometric parameters, background gas parameters, and surface material parameters of the target capacitively coupled plasma chamber, and use fluid simulation software to establish a fluid model. Solve the fluid model to obtain the spatio-temporal distribution of the ionization rate and the spatio-temporal distribution of the electromagnetic field.

[0058] Specifically, a capacitively coupled plasma (CCP) chamber is a plasma generation device widely used in the fields of microelectronics processing, material surface treatment, etc. It generates a high-density and uniformly distributed plasma in the chamber through capacitive coupling.

[0059] The geometric parameters include chamber size, chamber structure, electrode type, electrode spacing, chamber boundary position data, substrate position data, etc. The background gas parameters include the type, temperature, concentration, flow rate, etc. of the background gas. The surface material parameters include the materials of the chamber inner wall and the electrode materials. The fluid model is used to simulate the change process of the plasma in the target capacitively coupled plasma chamber over time and space. Use the particle transport solver in the fluid simulation software to solve the fluid model to obtain the spatio-temporal distribution of the ionization rate; use the electromagnetic field solver in the fluid simulation software to solve the fluid model to obtain the spatio-temporal distribution of the electromagnetic field. These data will serve as the basis for subsequent ion generation, ion motion simulation, and ion-background gas collision simulation. Among them, the spatio-temporal distribution of the ionization rate is used to reflect the rate at which background gas molecules in the target capacitively coupled plasma chamber are ionized to generate ions at different spatial positions and time points, and the spatio-temporal distribution of the electromagnetic field is used to reflect the change of the electromagnetic field in the target capacitively coupled plasma chamber over time and space. Note that this process is carried out in the CPU memory.

[0060] In one implementation, the fluid simulation software is COMSOL software.

[0061] Please refer to Figure 1 , the method for determining the ion energy angle distribution described in the embodiments of the present invention includes the following steps:

[0062] Step S200: Obtain ion collision cross-section data, where the ion collision cross-section data includes the collision cross-section values corresponding to various collision types between ions and background gas molecules.

[0063] Specifically, the present invention simulates the collision between ions and background gas molecules. Different collision types correspond to different collision cross-section values. The collision types include elastic collision, excitation, ionization, charge exchange, chemical reaction, etc. Obtain the ion collision cross-section data by importing it from an external data file as the basis for subsequent simulation of the collision between ions and background gas molecules. This part is also carried out in the CPU memory.

[0064] Please refer toFigure 1 , the method for determining the ion energy angle distribution according to the embodiment of the present invention further includes the following steps:

[0065] Step S300: Based on the electromagnetic field spatio-temporal distribution, the ionization rate spatio-temporal distribution, the ion collision cross-section data, and the geometric parameters, iteratively simulate the generation of ions, the ion movement, and the collision between ions and background gas molecules in the target capacitively coupled plasma chamber until the end condition is satisfied, and obtain the ion energy angle distribution of the ions reaching the substrate.

[0066] Specifically, after obtaining the ion collision cross-section data, it further includes: transmitting the electromagnetic field spatio-temporal distribution, the ionization rate spatio-temporal distribution, the ion collision cross-section data, and the geometric parameters to a fluid-particle hybrid model deployed in the GPU memory, and then using the fluid-particle hybrid model to perform simulation operations. In the prior art, the mesh particle method uses the CPU memory for parallel computing to solve the ion energy angle distribution, and usually faces the problem of load balancing. Due to the uneven distribution of particles, some CPU memories will process more particles, resulting in a reduction in the overall computing efficiency. To solve this problem, the present invention uses a fluid-particle hybrid model to calculate and simulate the movement and collision of particles. The present invention uses the large-scale parallel computing of the GPU to solve the load balancing problem of the mesh particle method running in the traditional CPU memory. The GPU has thousands of stream processors and can process thousands of threads simultaneously. For the simulation of particle movement and interaction, the GPU assigns a thread to each ion for calculation and simulation, significantly accelerating the calculation process with high parallelism and avoiding the load balancing problem of traditional CPU memory parallelism.

[0067] In one implementation, based on the electromagnetic field spatio-temporal distribution, the ionization rate spatio-temporal distribution, the ion collision cross-section data, and the geometric parameters, iteratively simulate the generation of ions, the ion movement, and the collision between ions and background gas molecules in the target capacitively coupled plasma chamber until the end condition is satisfied, and obtain the ion energy angle distribution of the ions reaching the substrate, including:

[0068] In each iteration, according to the ionization rate spatio-temporal distribution, simulate the generation of ions in the target capacitively coupled plasma chamber, and based on the electromagnetic field spatio-temporal distribution, the ion collision cross-section data, the geometric parameters, and the attribute information of each ion, simulate the ion movement and the collision between ions and background gas molecules in the target capacitively coupled plasma chamber;

[0069] When the end condition is satisfied, stop the iteration, and based on the energy and angle of the ions reaching the substrate in the last iteration, obtain the ion energy angle distribution of the ions reaching the substrate.

[0070] Specifically, the generation, movement, and collision of ions are simulated through multiple iterations.

[0071] In one implementation, according to the spatio-temporal distribution of the ionization rate, simulating the generation of ions in the target capacitively coupled plasma chamber includes:

[0072] According to the spatio-temporal distribution of the ionization rate, determine the ionization rate at the corresponding position in the target capacitively coupled plasma chamber at the current time step;

[0073] Accumulate the ionization rate at each corresponding position at the current time step and the ionization rate at the historical time step to obtain the ion generation progress corresponding to each corresponding position;

[0074] Compare the ion generation progress corresponding to each corresponding position with 1. If the ion generation progress at this corresponding position is equal to 1, simulate the generation of ions at this corresponding position.

[0075] Specifically, when the ion generation progress is 0, it means that no ions have been generated. When the ion generation progress is 1, it means that enough ion generation progress has been accumulated to generate one ion.

[0076] In one implementation, the geometric parameters include chamber boundary position data and substrate position data, and the attribute information includes mass, position, velocity, and charge; based on the spatio-temporal distribution of the electromagnetic field, the ion collision cross-section data, the geometric parameters, and the attribute information of each ion, simulating the movement of ions and the collision of ions with background gas molecules in the target capacitively coupled plasma chamber includes:

[0077] Based on the spatio-temporal distribution of the electromagnetic field and the charge of each ion, obtain the electromagnetic force received by each ion;

[0078] Based on the mass, position, velocity, and the electromagnetic force received by each ion, calculate and store the position and velocity of each ion after simulated movement;

[0079] Based on the position of each ion after simulated movement, the chamber boundary position data, and the substrate position data, determine the position state of each ion, where the position state includes detaching from the boundary of the target capacitively coupled plasma chamber, reaching the substrate, and being inside the target capacitively coupled plasma chamber and not reaching the substrate;

[0080] Delete the ions that have detached from the boundary of the target capacitively coupled plasma chamber, and record the position and angle of the ions that have reached the substrate;

[0081] Using the Monte Carlo method, determine whether the ions located inside the target capacitively coupled plasma chamber and not reaching the substrate collide with background gas molecules according to the ion collision cross-section data;

[0082] If a collision occurs, the velocity of the ion after the simulated collision and the position of the ion after the simulated movement are used as the velocity and position of the ion for the next iteration.

[0083] If no collision occurs, the velocity and position of the ion after the simulated movement are used as the velocity and position of the ion for the next iteration.

[0084] Specifically, during the simulation, in each iteration, ion generation by simulation, calculation of the electromagnetic force acting on the ions, simulation of ion movement, boundary processing (i.e., based on the position of each ion after the simulated movement, the position data of the chamber boundary, and the position data of the substrate, determining the position state of each ion, where the position state includes leaving the boundary of the target capacitively coupled plasma chamber, reaching the substrate, and being within the target capacitively coupled plasma chamber without reaching the substrate; deleting the ions that leave the boundary of the target capacitively coupled plasma chamber, and recording the position and angle of the ions that reach the substrate) and simulation of ion collisions with background gas molecules are performed in sequence.

[0085] In the prior art, in order to accurately capture the physical state of the system, the particle-in-cell method usually needs to simulate a huge system containing hundreds of thousands or even millions of particles. This method requires calculating each particle one by one, which undoubtedly brings a huge computational burden. In contrast, the present invention approximates the behavior of the plasma by simulating the movement and collision of macro-particles. Particle collisions mainly include collisions between charged particles and collisions between charged particles and the background gas. Given that the concentration of the background gas is much higher than that of the charged particles, the collision probability between charged particles is relatively low, so it is ignored in the simulation of the present invention to simplify the calculation process. In addition, the traditional particle-in-cell method needs to detail the tracking of the movement and collision of a large number of particles, which leads to a sharp increase in the amount of calculation. However, according to the existing theory, the energy-angle distribution function of the ions reaching the substrate is mainly affected by the electric field acceleration process when the ions cross the sheath layer and the ion collision events. Based on this, the present invention uses the ionization rate calculated by the fluid model to generate ions, rather than generating particles by simulating the ionization process of electrons. This strategy bypasses the tracking of electrons, thereby greatly reducing the number of particles to be processed in the particle simulation, and thus significantly saving the calculation time.

[0086] In one implementation, based on the spatio-temporal distribution of the electromagnetic field and the charge of each ion, the electromagnetic force acting on each ion is obtained, including:

[0087] Based on the spatio-temporal distribution of the electromagnetic field, the electric field strength and magnetic field strength at the position of each ion are calculated by an interpolation method;

[0088] Based on the electric field strength, the magnetic field strength and the charge of each ion, the electromagnetic force acting on each ion is obtained.

[0089] Specifically, through the interpolation algorithm, the spatial variation of the electromagnetic field can be captured more accurately, thereby calculating a more precise electromagnetic force.

[0090] In one implementation, based on the mass, position, velocity, and electromagnetic force of each ion, and storing the position and velocity of each ion after simulated motion, including:

[0091] Obtain a preset time step, and calculate the velocity of the ion after simulated motion based on the mass, position, electromagnetic force, and time step of each ion;

[0092] Obtain the position of the ion after simulated motion based on the position of the ion and the velocity of the ion after simulated motion.

[0093] Specifically, use the formula to calculate the velocity of the ion after simulated motion, where is the velocity of the ion before simulated motion, is the ion mass, is the electromagnetic force received by the ion, is the time step. Use the formula to calculate the position of the ion after simulated motion, where is the position of the ion before simulated motion.

[0094] In one implementation, using the Monte Carlo method, determine whether the ions located in the target capacitively coupled plasma chamber and not reaching the substrate collide with the background gas molecules according to the ion collision cross-section data, including:

[0095] Sum all the collision cross-section values in the ion collision cross-section data to obtain the total collision cross-section value;

[0096] Based on the total collision cross-section value, calculate the probability of each ion located in the target capacitively coupled plasma chamber and not reaching the substrate colliding currently;

[0097] Generate a first random number and compare it with the probability of each ion located in the target capacitively coupled plasma chamber and not reaching the substrate colliding currently, and the first random number is between 0 and 1;

[0098] If the first random number is less than the probability of the ion located in the target capacitively coupled plasma chamber and not reaching the substrate colliding currently, generate a second random number, determine the collision type of the ion based on the interval range where the second random number is located, and calculate based on the collision type to obtain the velocity of the ion after simulated collision;

[0099] If the first random number is greater than the probability of the ion colliding currently, maintain the velocity of the ion as the velocity after simulated ion motion.

[0100] Specifically, if the ion collision cross-section data includes the cross-sections of N collisions, and the cross-section values for each collision mode are respectively , then the total collision cross-section value is . Using the following formula Calculate the probability of each ion located in the target capacitively coupled plasma chamber and not reaching the substrate to undergo a collision currently. In the formula, exp represents the exponential function with the natural constant e as the base, and e is 2.71828.

[0101] Generate a first random number , if , then perform a collision and generate a second random number . According to The interval range where it is located determines the specific collision type that the particle undergoes. According to different collision types and the type of ions, the velocity of the ions after the simulated collision can be calculated.

[0102] In one implementation, the method further includes:

[0103] Transfer the ion energy angle distribution of the determined ions reaching the substrate from the GPU memory to the CPU memory, and perform normalization processing using the CPU memory and output it.

[0104] Specifically, outputting the processing result to the CPU memory can facilitate interaction with other programs or modules, and provide convenience for subsequent data analysis and scientific research. Using the ion energy angle distribution of the ions reaching the substrate can be used in the process of ion-assisted etching of chips. The present invention uses the CPU memory and the GPU memory to cooperate in processing and calculation, and can effectively maintain load balance. The schematic diagram of data processing on the CPU memory and the GPU memory in the present invention is as Figure 2 shown.

[0105] To verify the effect of the present invention, comparative calculations are respectively performed using the present invention and the traditional particle-in-cell method. Figure 3 FIG. is a comparison diagram of the ion energy distributions obtained by the particle-in-cell method and the method of the present invention for the upper substrate, Figure 4 FIG. is a comparison diagram of the ion energy distributions obtained by the particle-in-cell method and the method of the present invention for the lower substrate. In Figure 3 and Figure 4 , the red solid line is the calculation result of the traditional particle-in-cell method, and the blue dashed line is the calculation result of the hybrid model. It can be seen that the ion energy distributions obtained by the method of the present invention and the particle-in-cell method on the upper substrate and the lower substrate are basically the same. Please refer to Figure 5 and Figure 6, it can be seen that the ion angular distributions calculated by the two methods are also basically the same. However, the time taken by the present invention is 54.38 seconds, while the time taken by the particle-in-cell method exceeds one day. The time taken by the present invention is much less than that of the particle-in-cell method.

[0106] In summary, the present invention obtains and based on the geometric parameters, background gas parameters, and surface material parameters of the target capacitive coupling plasma chamber, uses fluid simulation software to establish a fluid model, solves the fluid model to obtain the spatio-temporal distribution of the ionization rate and the spatio-temporal distribution of the electromagnetic field; obtains ion collision cross-section data; iteratively simulates the generation of ions, the movement of ions, and the collision of ions and background gas molecules in the target capacitive coupling plasma chamber until the end condition is met, and obtains the ion energy angular distribution of the ions reaching the substrate. The present invention uses the ionization rate calculated by the fluid model to generate new ions, avoiding the simulation of the ionization process; the present invention uses the electromagnetic field calculated by the fluid model to drive the movement of particles, avoiding the calculation of charge density and the solution of the electromagnetic field, and can solve the problem of repeated coupling of particles and fields, effectively reducing the time for determining the energy angular distribution of the ions reaching the substrate.

[0107] In one embodiment, as Figure 7 shown, based on the above ion energy angular distribution determination method, the present invention also correspondingly provides an ion energy angular distribution determination device, including:

[0108] A fluid simulation module 100, configured to obtain and based on the geometric parameters, background gas parameters, and surface material parameters of the target capacitive coupling plasma chamber, use fluid simulation software to establish a fluid model, solve the fluid model to obtain the spatio-temporal distribution of the ionization rate and the spatio-temporal distribution of the electromagnetic field, where the spatio-temporal distribution of the ionization rate is used to reflect the rate at which background gas molecules in the target capacitive coupling plasma chamber are ionized to generate ions at different spatial positions and time points, and the spatio-temporal distribution of the electromagnetic field is used to reflect the change of the electromagnetic field in the target capacitive coupling plasma chamber over time and space;

[0109] A data acquisition module 200, configured to obtain ion collision cross-section data, where the ion collision cross-section data includes collision cross-section values corresponding to various collision types between ions and background gas molecules;

[0110] A distribution determination module 300, configured to iteratively simulate the generation of ions, the movement of ions, and the collision of ions and background gas molecules in the target capacitive coupling plasma chamber based on the spatio-temporal distribution of the electromagnetic field, the spatio-temporal distribution of the ionization rate, the ion collision cross-section data, and the geometric parameters until the end condition is met, and obtain the ion energy angular distribution of the ions reaching the substrate.

[0111] In one embodiment, the device further includes:

[0112] A first solving unit, configured to solve the fluid model by using a particle transport solver in the fluid simulation software, so as to obtain a spatio-temporal distribution of ionization rate;

[0113] A second solving unit, configured to solve the fluid model by using an electromagnetic field solver in the fluid simulation software, so as to obtain a spatio-temporal distribution of electromagnetic field.

[0114] In one embodiment, the distribution determination module includes:

[0115] An iteration unit, configured to, in each iteration, generate ions in the target capacitively coupled plasma chamber according to the spatio-temporal distribution of ionization rate, and simulate ion movement and collisions between ions and background gas molecules in the target capacitively coupled plasma chamber based on the spatio-temporal distribution of electromagnetic field, the ion collision cross-section data, the geometric parameters, and the attribute information of each ion;

[0116] A distribution determination unit, configured to stop iteration when an end condition is satisfied, and obtain an ion energy-angle distribution of ions arriving at the substrate based on the energy and angle of ions arriving at the substrate in the last iteration.

[0117] In one embodiment, the device further includes:

[0118] An ionization rate determination unit, configured to determine the ionization rate at a corresponding position in the target capacitively coupled plasma chamber at the current time step according to the spatio-temporal distribution of ionization rate;

[0119] An accumulation unit, configured to accumulate the ionization rate at a corresponding position in the current time step and the ionization rate at a historical time step, so as to obtain an ion generation progress corresponding to each corresponding position;

[0120] An ion generation unit, configured to compare the ion generation progress corresponding to each corresponding position with 1, and if the ion generation progress at the corresponding position is equal to 1, generate ions at the corresponding position.

[0121] In one embodiment, the geometric parameters include chamber boundary position data and substrate position data, and the attribute information includes mass, position, velocity, and charge; the device further includes:

[0122] An electromagnetic force calculation unit, configured to obtain the electromagnetic force received by each ion based on the spatio-temporal distribution of electromagnetic field and the charge of each ion;

[0123] A simulated movement unit, configured to calculate and store the position and velocity of each ion after simulated movement based on the mass, position, velocity, and received electromagnetic force of each ion;

[0124] A relationship determination unit, configured to determine the position state of each ion based on the position of each ion after simulated movement, the chamber boundary position data, and the substrate position data, where the position state includes being outside the boundary of the target capacitively coupled plasma chamber, reaching the substrate, and being inside the target capacitively coupled plasma chamber and not reaching the substrate;

[0125] A boundary processing unit, configured to delete the ions outside the boundary of the target capacitively coupled plasma chamber and record the positions and angles of the ions reaching the substrate;

[0126] A collision simulation unit, configured to use the Monte Carlo method to determine whether the ions inside the target capacitively coupled plasma chamber and not reaching the substrate collide with background gas molecules according to the ion collision cross-section data;

[0127] A first simulation result unit, configured to, if a collision occurs, use the velocity of the ion after simulated collision and the position of the ion after simulated movement as the velocity and position of the ion for the next iteration;

[0128] A second simulation result unit, configured to, if no collision occurs, use the velocity and position of the ion after simulated movement as the velocity and position of the ion for the next iteration.

[0129] In one embodiment, the device further includes:

[0130] An electromagnetic field determination unit, configured to calculate the electric field strength and magnetic field strength at the position where each ion is located by an interpolation method based on the spatio-temporal distribution of the electromagnetic field;

[0131] An electromagnetic force calculation unit, configured to obtain the electromagnetic force received by each ion based on the electric field strength, the magnetic field strength, and the charge of each ion.

[0132] In one embodiment, the device further includes:

[0133] A cross-section summation unit, configured to sum all the collision cross-section values in the ion collision cross-section data to obtain a total collision cross-section value;

[0134] A probability generation unit, configured to calculate the probability of each ion inside the target capacitively coupled plasma chamber and not reaching the substrate colliding currently based on the total collision cross-section value;

[0135] A comparison unit, configured to generate a first random number and compare it with the probability of each ion inside the target capacitively coupled plasma chamber and not reaching the substrate colliding currently, where the first random number is between 0 and 1;

[0136] A data update unit, configured to generate a second random number if the first random number is less than the probability of the ion that is located in the target capacitive coupling plasma chamber and has not reached the substrate colliding currently, determine the collision type of the ion based on the range of the interval where the second random number is located, and perform calculations based on the collision type to obtain the velocity of the ion after simulated collision;

[0137] A data maintenance unit, configured to maintain the velocity of the ion as the velocity after simulated ion movement if the first random number is greater than the probability of the ion colliding currently.

[0138] Based on the above embodiments, the present invention further provides a terminal, and its principle block diagram can be as Figure 8 shown. The above terminal includes a processor, a memory, a network interface, and a display screen connected through a device bus. Among them, the processor of the terminal is used to provide computing and control capabilities. The memory of the terminal includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating device and an ion energy angle distribution determination program. The internal memory provides an environment for the operation of the operating device and the ion energy angle distribution determination program in the non-volatile storage medium. The network interface of the terminal is used to communicate with an external terminal through a network connection. When the ion energy angle distribution determination program is executed by the processor, it implements the steps of any one of the above ion energy angle distribution determination methods. The display screen of the terminal can be a liquid crystal display screen or an electronic ink display screen.

[0139] Those skilled in the art can understand that Figure 8 the principle block diagram shown in

[0140] is only a block diagram of some structures related to the solution of the present invention, and does not constitute a limitation on the terminal to which the solution of the present invention is applied. The specific terminal may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0141] In one embodiment, a terminal is provided. The above terminal includes a memory, a processor, and an ion energy angle distribution determination program stored on the above memory and executable on the above processor. When the ion energy angle distribution determination program is executed by the above processor, it implements the steps of any one of the ion energy angle distribution determination methods provided by the embodiments of the present invention.

[0142] It should be understood that the sequence numbers of the steps in the above embodiments do not imply the order of execution. The order of execution of each process should be determined according to its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.

[0143] Those skilled in the art can clearly understand that for the convenience and brevity of description, only the above division of each functional unit and module is used as an example. In actual applications, the above functions can be allocated to different functional units and modules according to needs, that is, the internal structure of the above device is divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiment can be integrated into a processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above integrated unit can be implemented in the form of hardware or in the form of a software functional unit. In addition, the specific names of each functional unit and module are only for the convenience of mutual distinction and do not limit the protection scope of the present invention. The specific working process of the units and modules in the above device can refer to the corresponding process in the foregoing method embodiments and will not be elaborated herein.

[0144] In the above embodiments, the descriptions of the respective embodiments have their own emphases. For the parts not detailed or recorded in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0145] Those of ordinary skill in the art can realize that the units and algorithm steps of the examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or by a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods for each specific application to implement the described functions, but such implementation should not be considered to exceed the scope of the present invention.

[0146] In the embodiments provided by the present invention, it should be understood that the disclosed device / terminal device and method can be implemented in other ways. For example, the device / terminal device embodiments described above are only illustrative. For example, the above division of modules or units is only a logical function division. In actual implementation, there can be other division methods. For example, multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed.

[0147] The above-described embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not essentially depart from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for determining ion energy angle distribution, characterized in that: The method comprises: Acquire and establish a fluid model using fluid simulation software based on the geometric parameters, background gas parameters and surface material parameters of the target capacitively coupled plasma chamber, and solve the fluid model to obtain the spatiotemporal distribution of ionization rate and the spatiotemporal distribution of electromagnetic field; Acquiring ion collision cross section data, wherein the ion collision cross section data includes collision cross section values ​​corresponding to multiple collision types between ions and background gas molecules; Based on the spatiotemporal distribution of the electromagnetic field, the spatiotemporal distribution of the ionization rate, the ion collision cross-section data and the geometric parameters, iteratively simulate the generation of ions, the movement of ions and the collision of ions with background gas molecules in the target capacitively coupled plasma chamber until an end condition is met, thereby obtaining the ion energy angle distribution of ions arriving at the substrate; Among them, the spatiotemporal distribution of ionization rate is used to reflect the rate at which background gas molecules in the target capacitively coupled plasma chamber are ionized to generate ions at different spatial positions and time points, and the spatiotemporal distribution of electromagnetic field is used to reflect the change of electromagnetic field in the target capacitively coupled plasma chamber with time and space.

2. The method for determining ion energy angle distribution according to claim 1, characterized in that: Solving the fluid model to obtain the spatiotemporal distribution of ionization rate and the spatiotemporal distribution of electromagnetic field includes: Solving the fluid model using a particle transport solver in the fluid simulation software to obtain a spatiotemporal distribution of ionization rate; The fluid model is solved using the electromagnetic field solver in the fluid simulation software to obtain the spatiotemporal distribution of the electromagnetic field.

3. The method for determining ion energy angle distribution according to claim 1, characterized in that: Based on the spatiotemporal distribution of the electromagnetic field, the spatiotemporal distribution of the ionization rate, the ion collision cross-section data and the geometric parameters, iteratively simulate the generation of ions, the movement of ions and the collision of ions with background gas molecules in the target capacitively coupled plasma chamber until an end condition is met, and obtain the ion energy angle distribution of ions arriving at the substrate, including: In each iteration, according to the spatiotemporal distribution of ionization rate, simulating the generation of ions in the target capacitively coupled plasma chamber, and based on the spatiotemporal distribution of electromagnetic field, the ion collision cross section data, the geometric parameters and the property information of each ion, simulating the movement of ions and the collision of ions with background gas molecules in the target capacitively coupled plasma chamber; When the end condition is met, the iteration is stopped, and based on the energy and angle of the ions reaching the substrate in the last iteration, the ion energy angle distribution of the ions reaching the substrate is obtained.

4. The method for determining ion energy angle distribution according to claim 3, characterized in that: According to the spatiotemporal distribution of the ionization rate, simulating the generation of ions in the target capacitively coupled plasma chamber comprises: Determining the ionization rate of a corresponding position in the target capacitively coupled plasma chamber at a current time step according to the spatiotemporal distribution of the ionization rate; The ionization rate of each corresponding position in the current time step and the ionization rate of the historical time step are accumulated to obtain the ion generation progress of each corresponding position; The ion generation progress corresponding to each corresponding position is compared with 1. If the ion generation progress of the corresponding position is equal to 1, ion generation is simulated at the corresponding position.

5. The method for determining ion energy angle distribution according to claim 3, characterized in that: The geometric parameters include chamber boundary position data and substrate position data, and the attribute information includes mass, position, velocity and charge; based on the electromagnetic field spatiotemporal distribution, the ion collision cross-section data, the geometric parameters and the attribute information of each ion, simulating ion movement and collision between ions and background gas molecules in the target capacitively coupled plasma chamber, including: Based on the spatiotemporal distribution of the electromagnetic field and the charge of each ion, the electromagnetic force exerted on each ion is obtained; Based on the mass, position, velocity and electromagnetic force of each ion, the position and velocity of each ion after simulated motion are calculated and stored; Determine the position state of each ion based on the position of each ion after simulated movement, the chamber boundary position data, and the substrate position data, wherein the position state includes leaving the target capacitively coupled plasma chamber boundary, arriving at the substrate, and being located in the target capacitively coupled plasma chamber but not arriving at the substrate; Delete ions that escape from the target capacitively coupled plasma chamber boundary and record the position and angle of ions arriving at the substrate; Using the Monte Carlo method, judging whether the ions located in the target capacitively coupled plasma chamber and not reaching the substrate collide with the background gas molecules according to the ion collision cross section data; If a collision occurs, the velocity of the ion after the simulated collision and the position of the ion after the simulated motion are used as the velocity and position of the ion in the next iteration; If no collision occurs, the velocity and position of the ion after the simulated motion are used as the velocity and position of the ion in the next iteration.

6. The method for determining ion energy angle distribution according to claim 5, characterized in that: Based on the spatiotemporal distribution of the electromagnetic field and the charge of each ion, the electromagnetic force on each ion is obtained, including: Based on the spatiotemporal distribution of the electromagnetic field, the electric field strength and the magnetic field strength at the position of each ion are calculated by an interpolation method; Based on the electric field strength, the magnetic field strength and the charge of each ion, the electromagnetic force to which each ion is subjected is obtained.

7. The method for determining ion energy angle distribution according to claim 5, characterized in that: Using the Monte Carlo method, judging whether ions located in the target capacitively coupled plasma chamber and not reaching the substrate collide with background gas molecules according to the ion collision cross section data includes: summing all collision cross section values ​​in the ion collision cross section data to obtain a total collision cross section value; Based on the total collision cross section value, calculating the probability of each ion located in the target capacitively coupled plasma chamber and not reaching the substrate to collide at present; Generate a first random number and compare it with the probability of each ion currently colliding in the target capacitively coupled plasma chamber and not reaching the substrate, wherein the first random number is between 0 and 1; If the first random number is less than the probability of the ion that is located in the target capacitively coupled plasma chamber and has not reached the substrate colliding at present, a second random number is generated, a collision type of the ion is determined based on the interval range of the second random number, and a calculation is performed based on the collision type to obtain a velocity of the ion after the simulated collision; If the first random number is greater than the probability of the ion colliding at present, the speed of the ion is maintained at the speed after the simulated ion motion.

8. An apparatus for determining ion energy angle distribution, characterized in that: include: A fluid simulation module is used to obtain and establish a fluid model using fluid simulation software based on the geometric parameters, background gas parameters and surface material parameters of the target capacitively coupled plasma chamber, and solve the fluid model to obtain the spatiotemporal distribution of ionization rate and the spatiotemporal distribution of electromagnetic field. The spatiotemporal distribution of ionization rate is used to reflect the rate at which the background gas molecules in the target capacitively coupled plasma chamber are ionized to generate ions at different spatial positions and time points, and the spatiotemporal distribution of electromagnetic field is used to reflect the change of electromagnetic field in the target capacitively coupled plasma chamber with time and space; A data acquisition module, used to acquire ion collision cross section data, wherein the ion collision cross section data includes collision cross section values ​​corresponding to various collision types between ions and background gas molecules; The distribution determination module is used to iteratively simulate the generation of ions, ion movement and collision of ions with background gas molecules in the target capacitively coupled plasma chamber based on the spatiotemporal distribution of the electromagnetic field, the spatiotemporal distribution of the ionization rate, the ion collision cross-section data and the geometric parameters until the end condition is met to obtain the ion energy angle distribution of the ions arriving at the substrate.

9. A terminal, characterized in that: The terminal includes a memory, a processor, and an ion energy angle distribution determination program stored in the memory and executable on the processor. When the ion energy angle distribution determination program is executed by the processor, the steps of the ion energy angle distribution determination method as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores an ion energy angle distribution determination program, and when the ion energy angle distribution determination program is executed by a processor, the steps of the ion energy angle distribution determination method according to any one of claims 1 to 7 are implemented.

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