Min Uk Lee

We develop an explicit closed-form formulation for fluid plasma instabilities in magnetic-field geometries for near-bi-Maxwellian plasmas. Starting from the continuity, momentum, and anisotropic pressure equations, we derive a generalized closed-form expression for the imaginary part of the frequency, expressed in terms of spatial gradients of density, flow velocity, anisotropic pressures, and magnetic fields. The results demonstrate how electromagnetic wave behavior depends explicitly on geometric effects and pressure anisotropy arising from their intrinsic coupling, clarifying instability criteria that were not captured in previous fluid models. The analysis further reveals that non-plane wave effects can independently modify wave dynamics, even in the absence of spatial inhomogeneities. Taken together, these findings provide an analytic generalization that incorporates effects overlooked in conventional fluid formulations. Comparison with numerical solutions confirms the predictive capability of the analytic framework, demonstrating its ability to avoid the iterative and computational overhead required in traditional approaches. To demonstrate practical utility, we present complex dispersion relations and representative instability growth rates and criteria for plasma waves in nonuniform conditions, including circularly polarized, ordinary, extraordinary, whistler, and Alfvén modes, as well as electromagnetic modes in unmagnetized plasmas. The resulting formalism provides a precise and robust analytic framework for predicting plasma wave dispersion and instability properties, offering both direct physical interpretation and practical evaluation capability across fusion plasmas, space environments, and laboratory devices.

Voltage waveform tailoring is a promising approach for controlling charged-particle incidence in capacitively coupled plasmas (CCPs), particularly for high-aspect-ratio (HAR) dielectric etching where electron incidence with sufficient directionality, energy, and radial uniformity is required for charge compensation. Peak voltage waveforms can improve electron incidence by narrowing the electron angular distribution toward the surface-normal direction and shifting the electron energy distribution toward higher energies, but whether these favorable incident-electron distributions remain radially uniform in a two-dimensional electrode geometry remains unclear. Here, two-dimensional particle-in-cell/Monte Carlo collision simulations are used to investigate the radial uniformity of incident-electron angular and energy distributions under peak-waveform excitation. Increasing the harmonic content produces more surface-normal and higher-energy electron incidence in electrode-averaged distributions, but it also generates pronounced radial nonuniformity in the incident-electron angular and energy distributions across the powered electrode. This reveals a trade-off in which the electron-incidence enhancement produced by the conventional high-harmonic peak waveform is accompanied by degradation of radial uniformity. Spatiotemporal electric-field and electron-flux analyses show that residual temporal ripples in the conventional peak waveform excite an edge-driven radial electrostatic response, leading to spatially nonuniform electron fluxes and radial variations in the incident-electron distributions. We find that smoothing the peak waveform by reducing the relative contribution of higher-order harmonics suppresses these residual field and flux modulations while preserving the sheath-collapse acceleration responsible for surface-normal and high-energy electron incidence. As a result, the radial nonuniformity of the incident-electron angular and energy distributions is substantially reduced. These results demonstrate that peak-waveform control can be extended from electron-incidence enhancement to the improvement of radial uniformity, providing a kinetic simulation-based design principle for waveform-tailored CCPs used in HAR dielectric etching.

As low-temperature plasmas (LTPs) have gained significant attention in materials processing for the microelectronics industry, challenges in spatiotemporal analysis of plasma parameters in a radio frequency capacitively coupled plasma (RF-CCP) system necessitate multidimensional numerical simulations. This study investigated the conditions under which a kinetic simulation or a fluid model is effective for low-pressure CCPs, focusing on the critical role of energy-dependent electron kinetics in LTPs by comparing symmetric and asymmetric electrode structures. We provide a comprehensive investigation of particle energy distributions, elucidating the kinetic effects of non-Maxwellian distributions. The validity of standard fluid approximations, such as the drift–diffusion approximation and isotropic pressure assumptions, is assessed by comparing results from a two-dimensional fluid model with those from a particle-in-cell simulation. The dominance of the ion pressure tensor over isotropic approximations in the sheath has been observed, especially in an asymmetric electrode structure, which is more representative of realistic process chambers.

As low-temperature plasmas (LTPs) have gained significant attention in materials processing for the microelectronics industry, challenges in spatiotemporal analysis of plasma parameters in an RF capacitively coupled plasma (CCP) system necessitate multidimensional numerical simulations. This study investigated the conditions under which a kinetic simulation or a fluid model is effective for low-pressure CCPs, focusing on the critical role of energy-dependent electron kinetics in LTPs by comparing symmetric and asymmetric electrode structures. We provide a comprehensive investigation of particle energy distributions, elucidating the kinetic effects of non-Maxwellian distributions. The validity of standard fluid approximations, such as the drift-diffusion approximation and isotropic pressure assumptions, is assessed by comparing results from a two-dimensional fluid model with those from a particle-in-cell simulation. The dominance of the ion pressure tensor over isotropic approximations in the sheath has been observed, especially in an asymmetric electrode structure, which is more representative of realistic process chambers.

Establishing reliable scaling laws for plasma discharges is essential for the design of plasma devices, the development of processing recipes, and the advancement of plasma modeling. Within the extended Paschen framework, the breakdown voltage in radio-frequency (RF) capacitively coupled plasmas (CCPs) depends on the ratio of driving frequency to neutral pressure and on the gap-to-radius aspect ratio. The former relation has been well validated by experiments and numerical simulations, showing that the breakdown voltage remains constant when the frequency-to-pressure ratio is fixed. However, direct verification of the aspect-ratio scaling has been limited because systematic modification of electrode gap and radius is impractical in hardware. Here we present a numerical verification of the aspect-ratio scaling using two-dimensional fluid simulations over a wide pressure range for pure helium and argon-oxygen mixtures. Across pressures and chemistries, breakdown voltages converge when the aspect ratio is held constant, demonstrating geometric similarity in RF discharges, elucidating the role of reactor geometry in ignition, and revealing the explicit dependence of discharge characteristics on the aspect ratio. Furthermore, an aspect-ratio criterion governing the transition between discharge modes is identified. These results confirm the universality of the scaling under practical RF discharge conditions. This study provides a robust, physics-based scaling framework for the design and optimization of CCP reactors, supporting predictive design workflows, diagnostics, and more efficient process transfer.

Transformer coupled plasma (TCP) sources are widely used in etching processes due to their ability to generate low-pressure, highly uniform, and high-density plasma. However, byproducts generated during etching accumulate on chamber walls, degrading plasma reproducibility and increasing both the frequency and duration of cleaning steps, ultimately reducing process throughput. To address this, plasma-based dry cleaning is commonly employed. In conventional dry cleaning processes, however, ion kinetic energies and incidence angles are not actively controlled, which limits further improvement in cleaning performance. In this study, we propose a method to enhance cleaning efficiency in TCP chambers by modulating charged particle dynamics via Lorentz force control through externally applied magnetic fields. Fluid plasma simulations were conducted under various magnetic field configurations to identify efficient field strengths and geometric distributions that enhance ion kinetic energy flux and guide ion incidence angles into the optimal range for wall cleaning. Specifically, the simulations incorporated Maxwell coils installed along the chamber sidewalls to implement realistic magnetic field distributions and verify their effectiveness in controlling ion flux to the chamber walls. Cleaning performance was assessed based on the ion kinetic energy flux and average ion incidence angle on the wall. The results confirm that magnetic field-based control of ion dynamics is an effective strategy for improving the efficiency of plasma-based dry cleaning processes.

A new algorithm for molecular dynamics (MD) simulations is developed to optimize plasma particle distributions at given initial temperatures. By combining velocity scaling and reassignment, the method effectively eliminates the initial rise and oscillation in temperatures observed with randomly distributed positions. These rises and oscillations are undesired numerical artifacts observed in conventional plasma MD simulations, arising from unoptimized particle positions. The algorithm demonstrates temperature relaxation without initial rises or oscillations, as well as precise flow velocity relaxation, enabling accurate measurement of relaxation times. The code is accelerated using graphics processing units for parallel processing, enhancing the study of plasma dynamics. The proposed method for distributing physically valid particles in MD simulations enables accurate studies of intrinsic collision processes in plasmas, including the dynamics of strongly coupled plasmas, plasma–wave interactions, and transport phenomena in magnetized plasmas. The paper concludes with a discussion of potential applications and future enhancements to the algorithm.

A general method for solving the drift kinetic equations is developed to derive the closure and transport relations for electron-ion plasmas in an axisymmetric magnetic field with nested flux surfaces. By expanding the electron and ion distribution functions into Fourier series of general moments, the drift kinetic equations are converted to a coupled system of algebraic equations. By eliminating the fluid equations, the electron and ion systems are decoupled, allowing each system of equations to be solved separately for closures. The closure relations connect parallel heat flux density, friction force density, and viscosity to the radial and parallel gradients of density and temperature, the parallel gradient of flow velocity, and the parallel relative flow velocity of electrons and ions. When these closure relations are combined with the fluid equations, the fluid quantities are expressed in terms of the radial gradients of density and temperature, as well as the radial and parallel components of the electric field. This framework offers a robust approach to studying transport phenomena in electron-ion plasmas. The transport relations are expected to provide a foundation for investigating plasma rotation, including intrinsic rotation, in various tokamak systems and under different plasma conditions.

With the growing emphasis on three-dimensional (3D) vertical structures for enhancing the storage capacity and performance of 3D-NAND flash memory devices, precise control and prediction of process results to minimize process variability are important. Herein we predicted the layer thickness of an oxide/nitride (ON) dielectric stack for a 3D-NAND deposition process using artificial intelligence (AI). We investigated the key variables influencing the thicknesses of multiple dielectrics to propose strategies for mitigating thickness variation. We constructed a virtual metrology (VM) model based on status-variable identification (SVID) and optical emission spectroscopy (OES) data collected from plasma deposition equipment, and employed explainable AI (XAI) algorithms to interpret the significance of variables affecting the process results. XAI also supports the reliability of AI-predictive models for determining the thicknesses of the deposited multi-layered ON stack. Using variables derived from the SVID and OES data, the models for predicting oxide layer thickness, nitride layer thickness, and the thicknesses of both oxide and nitride layers achieved accuracies of 99%, 88% and 99%, respectively. This study highlights the importance of developing high-performance VM models and interpreting predictive outcomes for precise process control in semiconductor plasma processes.