Ion beam deposition simulation method

Abstract

The invention relates to the technical field of photoetching, in particular to an ion beam deposition simulation method. Air layer modeling is introduced in the ion beam deposition simulation process, the energy loss of deposited atoms in the transmission process is accurately considered, the physical authenticity of the simulation model is improved, initial energy is generated based on the acceptance and rejection sampling method, the final speed of the deposited atoms reaching the surface of the substrate is obtained, and the simulation precision is improved. According to the method, the transmission process of deposited atoms can be accurately simulated, the surface roughness after ion beam deposition can be predicted, the precision of deposition simulation is remarkably improved, and the real situation in the deposition process is fully restored, so that a high-precision simulation model is generated, the accuracy and practicability of the simulation model are improved, and the prediction precision of the surface roughness is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of photolithography, in particular to an ion beam deposition simulation method. BACKGROUND

[0002] With the continuous reduction of the size of semiconductor devices, the requirements for precision and quality of manufacturing processes are increasing. Ion beam deposition (IBD) as a high-precision thin film deposition technology is widely used in photolithography, microelectronic device manufacturing and optical thin film preparation because it can achieve atomic level control. In the ion beam deposition process, the energy, speed and interaction with the substrate surface of the deposited atoms directly affect the quality and performance of the thin film.

[0003] In the prior art, ion beam deposition simulation is usually based on Monte Carlo method or molecular dynamics simulation, combined with target sputtering model and deposition atom transmission model to predict thin film growth behavior. However, it is generally difficult to completely restore the real situation of the substrate and atomic deposition process, and it is inevitable to introduce respective errors, such as changes in speed and energy during atomic deposition process, which will increase the uncertainty of the calculation results, leading to deviations between the simulation results and the actual deposition process.

[0004] Therefore, there is an urgent need for an ion beam deposition simulation method that can accurately simulate to improve the accuracy and practicality of the simulation model. SUMMARY

[0005] In order to overcome the deviation caused by the difficulty in completely restoring the real situation of the substrate and atomic deposition process in the existing ion beam deposition simulation, the present application provides an ion beam deposition simulation method.

[0006] In a first aspect, the present application provides an ion beam deposition simulation method, the method comprising: generating a substrate model based on a preset initial condition; obtaining the final speed of the deposition atoms reaching the substrate surface through energy calculation; setting the deposition parameters of the deposition atoms based on the final speed, and obtaining a deposition simulation model after deposition simulation; wherein the energy calculation comprises: generating the initial energy of the deposition atoms leaving the target based on the acceptance-rejection sampling method, calculating the final energy of the deposition atoms reaching the substrate surface according to the loss energy of the deposition atoms passing through the air layer and the initial energy, and obtaining the final speed of the deposition atoms reaching the substrate surface according to the final energy.

[0007] According to a specific embodiment, in the above simulation method, the final speed of the deposition atoms reaching the substrate surface is calculated according to the final energy, specifically comprising: Randomly sampling the final energy, converting the sampled final energy into a velocity to obtain the final velocity.

[0008] According to a specific embodiment, in the simulation method, the lost energy is the energy lost by the deposited atoms passing through the air layer and colliding with other atoms present in the air layer.

[0009] According to a specific embodiment, in the simulation method, the deposition parameters include the generation region of the deposited atoms, the deposition speed, the running track, and the deposition process parameters and the number of deposition steps.

[0010] According to a specific embodiment, in the simulation method, the deposition simulation includes: Relaxing the substrate model at room temperature; Releasing the deposited atoms in a cycle until the deposition is completed; After deposition, stability relaxation is performed.

[0011] According to a specific embodiment, in the simulation method, the releasing the deposited atoms in a cycle until the deposition is completed specifically includes: Setting the number of cycles, randomly generating the incident coordinates of the deposited atoms according to the generation region of the deposited atoms; Setting the deposition speed of the deposited atoms according to the final velocity, and performing deposition based on the deposition step length; Entering the cycle after reaching the deposition step length, until the number of cycles is reached and the deposition is completed.

[0012] According to a specific embodiment, in the simulation method, the energy calculation is performed using Python software and a corresponding Python file is generated, the deposition simulation is performed using LAMMPS software, and the Python file is read through a Python interface to obtain the final velocity.

[0013] According to a specific embodiment, in the simulation method, the initial conditions include atom type, boundary condition, air layer parameter, atomic molar mass, mixed force field, interatomic potential, deposition temperature, and relaxation step number.

[0014] According to a specific embodiment, the simulation method further includes: Based on the obtained deposition simulation model, the surface roughness of the substrate after ion beam deposition is calculated, and compared with the actual surface roughness of the substrate after ion beam deposition, and the deposition parameters are adjusted and the deposition simulation model is optimized according to the comparison result.

[0015] In a second aspect, the present application provides a computer readable storage medium having stored thereon a computer program, which, when executed by a processor, causes a computer to perform the ion beam deposition simulation method according to any one of the preceding aspects.

[0016] Compared with the prior art, the present application has the following beneficial effects: The present application introduces air layer modeling in the ion beam deposition simulation process, accurately considers the energy loss of deposition atoms in the transmission process, improves the physical authenticity of the simulation model, and generates the initial energy based on the acceptance-rejection sampling method, and then obtains the final velocity of the deposition atoms reaching the substrate surface, which can accurately simulate the transmission process of the deposition atoms, significantly improves the accuracy of the deposition simulation, fully restores the real situation in the deposition process, and thus generates a high-precision simulation model, improves the accuracy and practicality of the simulation model. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 A flowchart of the ion beam deposition simulation method provided by the embodiment of the present application is shown in the figure; Figure 2 An initial energy distribution diagram of the deposition atoms in the ion beam deposition simulation method provided by the embodiment of the present application is shown in the figure; Figure 3 A simulation model diagram of 1000 steps of deposition in the ion beam deposition simulation method provided by the embodiment of the present application is shown in the figure; Figure 4 A simulation model diagram of 2000 steps of deposition in the ion beam deposition simulation method provided by the embodiment of the present application is shown in the figure; Figure 5 A simulation model diagram of 3000 steps of deposition in the ion beam deposition simulation method provided by the embodiment of the present application is shown in the figure; Figure 6 A substrate and roughness relationship diagram of different deposition angles in the ion beam deposition simulation method provided by the embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0018] The present application will be further described in conjunction with specific embodiments. However, it should not be understood that the scope of the above-mentioned subject matter of the present application is limited to the following embodiments, and any technology realized based on the content of the present application falls within the scope of the present application.

[0019] Most of the existing deposition simulation adopts thin film deposition based on molecular dynamics simulation, which predicts the deposition result by calculating the interaction force between atoms. It does not consider the energy loss of the deposition atoms when passing through the air layer, resulting in deviation between the simulation result and the actual deposition process, and the accuracy of the method for obtaining the initial energy distribution is limited, which makes it difficult to accurately reflect the physical characteristics of the target sputtering, and the model obtained by simulation cannot fully restore the real situation of the substrate and the atomic deposition process.

[0020] It can be understood that the deposition simulation generates a simulation model mainly to obtain a substrate surface consistent with the actual production situation and further measure the surface roughness to improve the production process of the substrate. In the existing substrate surface roughness measurement, including contact measurement and non-contact measurement, the former will cause the loss of the substrate surface and is not suitable for ultra-smooth surface, and the latter will be affected by the surface reflection effect and the material optical properties, resulting in deviation of the result. Therefore, there are great difficulties in the actual measurement of the substrate surface roughness.

[0021] The present application provides an ion beam deposition simulation method, which accurately simulates the transmission process of deposition atoms by introducing air layer modeling, generating initial energy based on acceptance rejection sampling method and energy loss calculation, thereby generating a high-precision simulation model, which can provide reliable guidance and reference for substrate surface roughness calculation.

[0022] The technical solutions provided by the present application will be further introduced and described below in combination with the drawings.

[0023] Please refer to Figure 1 which shows a flowchart of an ion beam deposition simulation method provided by an embodiment of the present application, the method comprising: Step 1: generating a substrate model based on preset initial conditions.

[0024] In a possible implementation manner, the LAMMPS software is used in the embodiment of the present application, and after the initial conditions are set, the simulation is started. The initial conditions include atomic type, boundary condition, air layer parameter, atomic molar mass, mixed force field, interatomic potential, deposition temperature and relaxation step number. After the simulation is started, a relatively stable bottom structure, i.e. the substrate model, can be generated.

[0025] Step 2: obtaining the final velocity of the deposition atoms reaching the substrate surface through energy calculation.

[0026] Generally, the deposition atoms are emitted to the target material by the emitter, and are sputtered and separated when passing through the target material, and then reach the substrate surface. In order to make the finally obtained deposition model consistent with the actual situation, the final velocity of the deposition atoms before reaching the substrate needs to be obtained through energy calculation. The velocity of the deposition atoms during deposition is controllable.

[0027] Specifically, the energy calculation includes: generating the initial energy of the deposition atoms leaving the target material based on the acceptance rejection sampling method, calculating the final energy of the deposition atoms reaching the substrate surface according to the energy loss of the deposition atoms passing through the air layer and the initial energy, and obtaining the final velocity of the deposition atoms reaching the substrate surface according to the final energy.

[0028] In the embodiments of the present application, the rejection sampling method is performed according to the Thomson formula. It can be understood that the Thomson formula describes the initial energy probability distribution of the metal atoms when leaving the target in the sputtering process, and the rejection sampling method is a method for generating random samples, which generates candidate points through a simple proposal distribution, and then determines whether to accept these points according to the target distribution (i.e. the distribution according to the Thomson formula).

[0029] In one possible implementation, a uniform distribution is selected as the proposal distribution, i.e. the probability of each energy value is equal in the range of 0 to the upper limit of the energy. Further, the maximum value of the ratio of the target distribution to the proposal distribution is calculated, which occurs when the energy is equal to half of the surface binding energy. Through numerical calculation, a constant is determined to ensure that the target distribution is always covered by the curve of the proposal distribution multiplied by the constant. Then the sampling is performed.

[0030] Specifically, the sampling process includes: randomly generating a candidate energy value from a uniform distribution; calculating the probability value of the energy under the Thomson distribution; generating a random number between 0 and 1 to determine whether to accept the candidate energy: if the random number is less than the ratio of the target distribution probability to the constant multiplied by the proposal distribution probability, then the energy is accepted; otherwise, it is rejected and resampled; repeat the above steps until a sufficient number of energy samples are generated, and the energy values of the energy samples are taken as the initial energies.

[0031] Further, after the deposition atom leaves the target, it enters the air layer before reaching the substrate, at which time other atoms exist in the air layer. By calculating the energy loss of the deposition atom passing through the air layer and colliding with other atoms existing in the air layer, combined with the initial energy when leaving the target, the energy of the deposition atom when reaching the substrate surface, i.e. the final energy, can be obtained.

[0032] Finally, the final energy is randomly sampled, and the sampled final energy is converted into velocity to obtain the final velocity. Specifically, a random selection is made among the above calculated final energies, and the energy value randomly selected is substituted into the kinetic energy formula to calculate the corresponding velocity value, i.e. the final velocity. Then the obtained final velocity is substituted into the deposition parameters in the deposition simulation, and the deposition simulation can be performed.

[0033] Step 3: Set the deposition parameters of the deposition atom based on the final velocity, and obtain the deposition simulation model after the deposition simulation.

[0034] Specifically, the deposition parameters include the generation region of the deposition atom, the deposition speed, the running trajectory, and the deposition process parameters and the deposition step number. After setting the deposition parameters, the deposition simulation can be started, and the specific steps of the deposition simulation include: Relaxing the substrate model at room temperature; Releasing deposition atoms in cycles until deposition is completed; Stability relaxation after deposition.

[0035] It can be understood that the stability relaxation is a simulation of the initial constructed system for a period of time, with the purpose of allowing the system to reach a stable, near-equilibrium state. Among them, the releasing deposition atoms in cycles until deposition is completed specifically includes: Setting the number of cycles, randomly generating the incident coordinates of the deposition atoms according to the generation area of the deposition atoms; Setting the deposition speed of the deposition atoms according to the final speed, and depositing based on the deposition step; Entering the cycle after reaching the deposition step, until the number of cycles is reached and the deposition is completed.

[0036] After the above steps are completed, a simulation model consistent with the real situation is obtained. In one possible implementation, the embodiment of the present application further includes calculating the substrate surface roughness after ion beam deposition based on the obtained deposition simulation model, and comparing it with the actual substrate surface roughness after ion beam deposition, adjusting the deposition parameters and optimizing the deposition simulation model according to the comparison result.

[0037] Based on the above technical solution, the present application introduces air layer modeling in the ion beam deposition simulation process, accurately considers the energy loss of deposition atoms in the transmission process, improves the physical reality of the simulation model, and generates the initial energy based on the acceptance-rejection sampling method, and then obtains the final speed of the deposition atoms reaching the substrate surface, which can accurately simulate the transmission process of the deposition atoms and predict the surface roughness after ion beam deposition, significantly improve the accuracy of the deposition simulation, fully restore the real situation in the deposition process, and thus generate a high-precision simulation model, improve the accuracy and practicality of the simulation model, and improve the prediction accuracy of the surface roughness.

[0038] The technical solutions provided by the present application will be further introduced and described in combination with specific embodiments. Al2O3 is used as a wafer substrate, and Cr atoms are used as deposition atoms. The deposition simulation is performed in the LAMMPS software.

[0039] As in step 1 above, a relatively stable substrate model is obtained for deposition simulation based on the preset initial conditions. The settings in the LAMMPS software are shown in Table 1.

[0040] Table 1: Substrate model generation setting table

[0041] Specifically, a substrate model of a sapphire (Al2O3) c0001 crystal surface is constructed by using Materials Studio, a third-generation charge optimized many-body (COMB3) is used as the potential function, and the model is relaxed for 20000 steps in an nvt ensemble at a temperature of 298K to obtain a relatively stable structure. It can be understood that the nvt system is a canonical system, which is applied to a system under an actual temperature environment with a fixed particle number, volume and temperature.

[0042] A Mixed Element Atomistic Method (MEAM) is used as the potential function between deposited metal atoms, and a Lennard-Jones potential (LJ) is used as the potential function between the deposited metal atoms and Al atoms and O atoms of the substrate. The deposition speed of the deposited atoms is set to 10-12 Å / ps, and the direction is parallel to the z-axis, and one atom is placed every 100 steps (1 ps). Wherein, ps is picosecond, indicating time step.

[0043] As in step 2 above, the final speed of the deposited atoms reaching the substrate surface is obtained. Considering that the deposited atoms have a certain energy when they reach the substrate surface by sputtering from the target, the energy distribution can be obtained by the Thomson formula: , Wherein, E 0 represents the initial energy of the deposited atoms when they leave the target, E b represents the binding energy of the deposited atoms, E Ar represents the energy of argon atoms, which is approximately equal to the radio frequency source voltage, represents the kinetic energy mass transfer factor. By using the rejection sampling method in Monte Carlo, the initial energy E0 distribution of the deposited atoms (taking Cr as an example) can be obtained. Please refer to Figure 2 , which shows the initial energy distribution of the deposited atoms according to an embodiment of the present application.

[0044] Next, the energy lost by the deposited atoms in the Ar environment through collision with argon atoms is calculated, that is, the final energy of the deposited atoms reaching the substrate surface is obtained, and the formula is: , , Wherein, represents the final energy of the deposited atoms reaching the substrate, is the gas energy to meet the Maxwell-Boltzmann energy distribution, represents the energy ratio of the deposited atoms and the gas atoms before and after a single collision, represents the total number of atomic collisions, represents the distance from the target to the substrate, represents the ambient cavity pressure, represents the collision cross section of the hypothetical hard-core interaction, K B represents the Boltzmann constant, T g represents the ambient temperature.

[0045] Further, the final energy obtained above is randomly extracted, and the extracted final energy is converted into a corresponding speed value through a kinetic energy formula, that is, a final speed is obtained. The calculation formula is: , wherein, represents the final speed, represents the final energy obtained by random sampling, represents the relative mass of the atom. The obtained final speed is substituted into the deposition parameters of the deposited atom, and simulation can be performed.

[0046] In one possible implementation, the above energy calculation is calculated by using Python software, and a corresponding Python file is generated. The Python file is read by using a Python interface in LAMMPS software, so that the deposition rate can be controlled.

[0047] Further, the energy calculation is shown in Table 2.

[0048] Table 2 Energy calculation table

[0049] As described above in step 3, the final speed is read from the above Python file, and deposition simulation is performed. Further, the deposition simulation process is shown in Table 3.

[0050] Table 3 Deposition simulation setting table

[0051] Please refer to Figures 3 to 5 which respectively show the schematic diagrams of the simulation models of different deposition steps provided by the embodiments of the present application. The surface roughness is calculated, and the root mean square roughness is calculated:

[0052] wherein, represents the root mean square roughness value, represents the total number of particles, represents the coordinate height of each deposited atom, represents the average value of the deposited atom coordinates. As Figure 3As shown, the surface roughness is about 0.02396 after deposition of 1000 steps. Figure 4 As shown, the surface roughness is about 0.017426 after deposition of 2000 steps. Figure 5 As shown, the surface roughness is about 0.011886 after deposition of 3000 steps. The error between the above roughness result and the experimental measured value is within ±0.1 nm, indicating the repeatability of the simulation result.

[0053] The ion beam deposition simulation method provided by the embodiment of the application fully restores the real situation in the deposition process, and thus can provide reliable guidance for the production process of the substrate. Based on this, the embodiment of the application can also be used for substrate roughness verification in other aspects. For example, the influence of deposition atoms on roughness at different incident angles can be verified. Specifically, the roughness at different angles can be obtained by rotating the angle of the substrate. Al2O3 is used as the substrate in the model establishment, and the substrate is rotated at 0°, 5°, 10°, 15°, 20° and 25°, respectively. The deposition atoms can be released at 2ps each time, and 10000 cycles are performed, with a total deposition time of 20ns.

[0054] Please refer to Figure 6 which shows the relationship between the substrate and the roughness at different deposition angles according to the embodiment of the application. As shown in the figure, the deposition angle has a certain influence on the roughness of the film layer. When the angle between the substrate and the target material changes from 0° to 25°, the roughness of the surface of the substrate generally shows a trend of first decreasing and then increasing, which is basically the same as the theoretical value trend obtained by simulation calculation. It is further illustrated that the simulation method provided by the application can obtain a high-precision simulation model and prediction result. The specific data is shown in Table 4.

[0055] Table 4: Experimental and theoretical values of substrate roughness at different deposition angles

[0056] On the other hand, the application also provides a computer readable storage medium having a computer program stored thereon, wherein the computer program is executed by a processor to make the computer execute the ion beam deposition simulation method according to any one of the above embodiments.

[0057] It can be understood that the technical solutions of the present application can be embodied in the form of a software product in essence or in the form of a part of the prior art or a part of the technical solutions, and the computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in various embodiments of the present application. The foregoing storage medium includes a U disk, a mobile hard disk, a ROM, a RAM, a magnetic disk or an optical disk, and various media that can store program codes.

[0058] Any embodiment or design described as "example" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or advantageous than other embodiments or design solutions. Rather, the word "example" or "for example" is used to present relevant concepts in a specific manner, facilitating understanding.

[0059] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. An ion beam deposition simulation method, characterized in that, The method includes: Generate a substrate model based on preset initial conditions; The final velocity of the deposited atoms reaching the substrate surface is obtained through energy calculations; Based on the final velocity, the deposition parameters of the deposited atoms are set, and a deposition simulation model is obtained after deposition simulation. The energy calculation includes: The initial energy of the deposited atom leaving the target is generated based on the accept-reject sampling method. The final energy of the deposited atom reaching the substrate surface is calculated based on the energy lost by the deposited atom through the air layer and the initial energy. The final velocity of the deposited atom reaching the substrate surface is obtained based on the final energy.

2. The ion beam deposition simulation method according to claim 1, characterized in that, The final velocity of the deposited atoms reaching the substrate surface is calculated based on the final energy, specifically including: The final energy is randomly sampled, and the sampled final energy is converted into velocity to obtain the final velocity.

3. The ion beam deposition simulation method according to claim 1, characterized in that, The energy loss refers to the energy lost by deposited atoms as they pass through the air layer and collide with other atoms present in the air layer.

4. The ion beam deposition simulation method according to claim 1, characterized in that, The deposition parameters include the generation region of the deposited atoms, the deposition rate, the trajectory, as well as the deposition process parameters and the number of deposition steps.

5. The ion beam deposition simulation method according to claim 1, characterized in that, The deposition simulation includes: The substrate model was relaxed at room temperature; The deposited atoms are released in a cycle until deposition is complete; After deposition, stability relaxation is performed.

6. The ion beam deposition simulation method according to claim 5, characterized in that, The cyclic release of deposited atoms until deposition is complete specifically includes: Set the number of cycles, and randomly generate the incident coordinates of the deposited atoms based on the generation region of the deposited atoms; The deposition rate of the deposited atoms is set according to the final velocity, and deposition is performed based on the deposition step size; Once the deposition step length is reached, the cycle begins until the required number of cycles is reached and deposition is complete.

7. The ion beam deposition simulation method according to claim 1, characterized in that, The energy calculation is performed using Python software, and a corresponding Python file is generated. The deposition simulation is performed using LAMMPS software, and the final velocity is obtained by reading the Python file through the Python interface.

8. The ion beam deposition simulation method according to claim 1, characterized in that, The initial conditions include atom type, boundary conditions, air layer parameters, atomic molar mass, mixing force field, interatomic potential, deposition temperature, and relaxation step number.

9. The ion beam deposition simulation method according to any one of claims 1 to 8, characterized in that, The method further includes: The surface roughness of the substrate after ion beam deposition is calculated based on the obtained deposition simulation model and compared with the surface roughness of the substrate after actual ion beam deposition. The deposition parameters are adjusted and the deposition simulation model is optimized based on the comparison results.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it causes the computer to perform the ion beam deposition simulation method as described in any one of claims 1 to 9.

Images