CN-121980728-A - Numerical simulation method for two-dimensional Ar-He mixed gas capacitively coupled plasma discharge

CN121980728ACN 121980728 ACN121980728 ACN 121980728ACN-121980728-A

Abstract

The invention discloses a numerical simulation method for two-dimensional Ar-He mixed gas capacitively coupled plasma discharge, and belongs to the technical field of plasma numerical simulation. The method combines a particle grid method and a Monte Carlo collision method, circularly executes the method at each time step by initializing a gas environment and a two-dimensional grid, distributes charge and electric field interpolation by utilizing an area weight method, solves a Poisson equation by adopting an SOR method, updates particle motion by using a frog-leaping method, processes boundary effect and specific collision event, counts ion energy distribution reaching an electrode after the system is stabilized, judges whether the ion energy distribution is unimodal distribution, and outputs key data for guiding process optimization, such as ion energy, ion flux, plasma uniformity and surface morphology control based on the distribution. The method overcomes the defect that the one-dimensional model ignores the radial effect, accurately simulates the cooperative discharge mechanism of Ar-He mixed gas, provides high-precision key data for optimizing the semiconductor plasma process, and has important practical value.

Inventors

CHEN YONG
HU YONG
Cui Chengshuai
LI PING
CHEN YANWEN
LIU YUXING

Assignees

安徽理工大学

Dates

Publication Date: 20260505
Application Date: 20251127

Claims (10)

1. The numerical simulation method of the two-dimensional Ar-He mixed gas capacitively coupled plasma discharge is characterized by comprising the following steps of: S1, distributing Ar-He mixed gas proportion in a cavity, and carrying out grid division on the cavity; S2, distributing the charges of the charged particles in each grid to surrounding grid points through an area weight method in each time step to obtain charge density distribution; S3, interpolating the electric field on the grid points to the charged particles through an area weight method, superposing the electric field with an externally applied radio frequency electric field, calculating the force borne by the charged particles, and updating the speed and the position of the charged particles; S4, judging whether the charged particles reach the boundary of the chamber, and carrying out absorption, reflection or secondary electron emission treatment on the charged particles reaching the boundary; S5, judging whether the charged particles collide with neutral gas particles, and if so, updating the state of the charged particles according to the collision type; S6, repeating the steps S2-S5 until the system reaches a steady state, and acquiring data distribution of charged particles in the steady state; S7, counting ion energy distribution at the electrode under the steady state, judging the ion energy distribution to be unimodal distribution in a test energy range, and outputting key data of ion energy, ion flux, plasma uniformity and surface morphology control based on the distribution.
2. The method for numerical simulation of two-dimensional Ar-He mixed gas capacitively coupled plasma discharge according to claim 1, wherein in the step S7, the unimodal distribution is determined as having only one global maximum and no second local peak in the ion energy distribution curve within a preset energy sampling range; The same energy resolution and sampling statistical time are adopted for judgment so as to ensure the consistency of criteria.
3. The method for numerical simulation of two-dimensional Ar-He mixed gas capacitively coupled plasma discharge according to claim 1, wherein in step S1, the density of argon in the Ar-He mixed gas And density of helium Is determined by the following formula: ; ; Wherein, the Is the gas pressure; is the boltzmann constant; is the gas temperature; is the proportion of argon in the mixed gas; Is the proportion of helium in the mixed gas.
4. The method for numerical simulation of two-dimensional Ar-He mixed gas capacitively coupled plasma discharge according to claim 1, wherein in step S1, the grid division satisfies that a length of each grid does not exceed a Debye length of the charged particles.
5. The method for numerical simulation of two-dimensional Ar-He mixed gas capacitively coupled plasma discharge according to claim 1, wherein in step S2, a Poisson' S equation is solved by adopting a successive super relaxation SOR iteration method.
6. The numerical simulation method of two-dimensional Ar-He mixed gas capacitively coupled plasma discharge according to claim 1, wherein in step S3, updating the velocity and position of charged particles is performed by using a frog-leaping method: The velocity of the particles is updated at half integer time steps and the position of the particles is updated at integer time steps.
7. The method for numerical simulation of two-dimensional Ar-He mixed gas capacitively coupled plasma discharge according to claim 1, wherein in step S4, whether electrons reaching an electrode are reflected or not is judged according to a random number, and whether secondary electrons are generated or not is judged according to a random number for the ions reaching the electrode.
8. The numerical simulation method of a two-dimensional Ar-He mixed gas capacitively coupled plasma discharge according to claim 1, wherein in step S5, the total probability of collision of electrons with neutral gas Calculated by the following formula: ; Wherein, the And The total section of collision of electrons and argon and the total section of collision of electrons and helium are respectively; as the relative velocity between electron and neutral particle collisions, The electron velocity is often taken; In time steps.
9. The numerical simulation method of a two-dimensional Ar-He mixed gas capacitively coupled plasma discharge according to claim 1, wherein in step S5, total probability of collision of ions with neutral gas Calculated by the following formula: ; Wherein, the The total section of Ar ion/He ion collision with argon gas; the total section of collision of Ar ion/He ion and helium gas; is the relative velocity between Ar ion/He ion and argon collision; Is the relative velocity between Ar ion/He ion and helium collision; The number of steps for ion sub-cycle; In time steps.
10. The method for numerical simulation of two-dimensional Ar-He mixed gas capacitively coupled plasma discharge according to claim 1, wherein the outputted surface morphology control key data comprise ion energy distribution unimodal judgment results which can be used for process window selection and ion flux and uniformity distribution corresponding to the ion energy distribution unimodal judgment results, and the data are stored in a file or database record form for process optimization calling.

Description

Numerical simulation method for two-dimensional Ar-He mixed gas capacitively coupled plasma discharge Technical Field The invention belongs to the technical field of plasma physical numerical simulation, and particularly relates to a two-dimensional particle simulation method for a capacitive coupling plasma discharge process, in particular to a numerical simulation method for two-dimensional capacitive coupling plasma discharge of Ar-He mixed gas. Background The fourth state of matter, plasma, plays a vital role in the industrial fields of semiconductor fabrication, material surface treatment, thin film deposition, etching, and the like. Among them, the capacitively coupled plasma source is widely used in processes such as etching, thin film deposition, sputtering, etc., because of its simple structure and easy generation of large-area uniform plasma. In practical processes, parameters of the plasma, such as ion energy, ion flux, electron temperature, and spatial uniformity, directly determine the quality and uniformity of the processing effect. In order to meet the diversified process requirements, it is important to precisely regulate the discharge process, and this often depends on a means of combining deep theoretical analysis, numerical simulation and experimental diagnosis. However, single gas discharge has inherent limitations such as limited discharge efficiency, narrow process window, insufficient stability, and the like, and is difficult to adapt to complex application scenes. To overcome these drawbacks, industry and academia is gradually turned to using mixed gas discharge strategies to improve discharge characteristics by synergistic effects between gas components, such as optimizing electron heating patterns, enhancing stability, and widening process flexibility. In addition, in the field of semiconductor precision processing, not only is plasma required to have high density and good uniformity, but also the ion energy distribution profile to the substrate is precisely required. For example, in nano-scale etching or ultra-thin film deposition, a broad or multimodal ion energy distribution may result in a non-uniform etch profile or reduced film quality. The argon ion energy distribution generated by single argon discharge is often wider or shows double peaks, which is not beneficial to the improvement of the process precision. Although helium is introduced to improve the stability of plasma and reduce the sputtering damage to the surface of the electrode, how to predict and guide and optimize the ratio of Ar-He mixed gas through accurate numerical simulation, so that ideal unimodal ion energy distribution which can be used for improving the process accuracy is obtained, and a complete scheme for outputting surface morphology control key data is synchronously established, so that the method has become a specific technical problem to be solved urgently in the field. The existing one-dimensional simulation or general two-dimensional simulation method does not relate to accurate judgment of 'single peak' and 'non-single peak' of ion energy distribution in a steady state, and also fails to correlate and output the judgment and key data of surface morphology control, so that direct and quantized simulation basis cannot be provided for selection of a high-precision process window. Among the numerous combinations of gases, the mixed use of argon and helium presents the unique advantages of having a higher ionization cross section and lower ionization energy, facilitating the efficient generation of plasma and promoting energy transfer, while helium, by virtue of its excellent thermal conductivity and chemical inertness, contributes to maintaining a low temperature steady state of plasma and reducing pollution to sensitive workpieces, and is particularly suitable for micromachining processes with stringent requirements on high precision and cleanliness. Despite these potential advantages, the complex interactions during the discharge process, particularly the collision kinetics between different particles, present challenges for accurately understanding and predicting their behavior. Most of the existing numerical simulation researches are based on one-dimensional models, and the models have higher calculation efficiency, but inevitably neglect key radial effects in the discharging process, such as edge sheath formation, radial diffusion of plasmas, non-uniformity of power deposition and the like. This simplification may lead to significant deviations from the actual situation in predicting the plasma density spatial distribution, ion flux at the electrode edge, and energy distribution, etc., which may not meet the need for fine optimization of process uniformity. In addition, although particle simulation methods, such as a particle grid method and a Monte Carlo collision method, are powerful tools for simulating plasma micromanipulation, the existing general simulation framework often lacks of target