arXiv subjects

Alexander Khrabrov

Publications and source records attributed to Alexander Khrabrov.

9 recordsLinked to original sources

arXiv2025

Particle-In-Cell Informed Kinetic Modeling of Nonlinear Skin Effects in Low-Frequency Inductively Coupled Plasmas

We perform extensive 2D Particle-In-Cell (PIC) electromagnetic simulations of low pressure Inductively Coupled Plasma (ICP) discharges with various coil current and driving frequencies. Our simulations show that in low-frequency cases, electrons in the skin region near the coil can be predominantly magnetized by the Radio Frequency (RF) magnetic field. More specifically, the electrons are trapped in the combined potential well formed by the vector and electrostatic potentials, where they oscillate for most of the RF period while drifting perpendicular to the RF magnetic field. When the magnetic field weakens, electrons shortly demagnetize, leading to jet-like currents and periodic bursts of energy deposition. Based on the newly discovered electron trajectories, we develop a new kinetic theory for the plasma skin effect in low-frequency Inductively Coupled Plasma (ICP) discharges, incorporating nonlinear electron motion in an RF magnetic field by integrating Vlasov equation along the unperturbed particle trajectory. This theory successfully predicts the time evolution of electron currents in low-frequency ICP plasmas, as well as a nonlinear relation between electron current and the RF inductive electric field in the new regime we found. Furthermore, by coupling this new kinetic theory with a global model, we provide a straightforward method for estimating equilibrium electron temperature, plasma density and electron current. These analytical predictions match well with our 2D PIC simulations and can be validated through future experimental studies.

physics.plasm-ph↗

arXiv2025

Nonlinear skin effect regime when a radio frequency electromagnetic field penetrates into a background plasma

Two-dimensional, electromagnetic particle-in-cell simulations are employed to study particle kinetics and power deposition in the skin layer when a Radio Frequency (RF) electromagnetic field penetrates into a background plasma. We identify a new regime at low frequency ($\sim\mathrm{MHz}$) and low pressure, where the motion of electrons can be highly nonlinear in the skin region. Through most of the RF cycle, the electrons are trapped in the effective potential formed by the vector and electrostatic potentials, with energy deposition being small and magnetic moment $μ$ no longer being an adiabatic invariant. However, for a brief period around the null of the oscillating magnetic field, the electrons get detrapped, causing a jet-like current penetrating into the bulk plasma. During these brief periods, the power deposition becomes high, exhibiting a periodic burst nature. Based on kinetic theory, we provide analytical expressions for the plasma current and energy deposition in the new regime. A criterion for transition between the newly identified low-frequency, periodic-burst regime and the usual anomalous non-local skin effect regime is proposed and verified.

physics.plasm-ph↗

arXiv2024

Investigating Instabilities in Magnetized Low-pressure Capacitively-Coupled RF Plasma using Particle-in-Cell (PIC) Simulations

The effect of a uniform magnetic field on particle transport in low-pressure radio frequency (RF) capacitively coupled plasma (CCP) has been studied using a particle-in-cell (PIC) model. Three distinct regimes of plasma behavior can be identified as a function of the magnetic field. In the first regime at low magnetic fields, asymmetric plasma profiles are observed within the CCP chamber due to the effect of E x B drift. As the magnetic field increases, instabilities develop and form self-organized spoke-shaped structures that are distinctly seen within the bulk plasma closer to the sheath. In this second regime, the spoke-shaped coherent structures rotate inside the plasma chamber in the - E x B direction, where E and B are the DC electric and magnetic field vectors, respectively, and the DC electric field exists in the sheath and pre-sheath regions. The spoke rotation frequency is in the MHz range. As the magnetic field strength increases further, the rotating coherent spokes continue to exist near the sheath. The coherent structures are, however, accompanied by new small-scale incoherent structures originating and moving within the bulk plasma region away from the sheath. This is the third regime of plasma behavior. The threshold values of the magnetic field between these regimes were found not to vary with changing plasma reactor geometry (e.g., area ratio between ground and powered electrodes) or the use of an external capacitor between the RF-powered electrode and the RF source. The threshold values of the magnetic field between these regimes shift toward higher values with increasing gas pressure. This paper provides guidance on the upper limit of the magnetic field for instability-free operation in low-pressure CCP-based semiconductor deposition and etch systems that use the external magnetic field for plasma uniformity control.

physics.plasm-ph↗

arXiv2023

Particle-in-cell simulation of a 50~mTorr capacitively coupled argon discharge over a range of frequencies

The effect of driving frequency in the range of 13.56 MHz to 73 MHz on electron energy distribution and electron heating modes in a 50 mTorr capacitively coupled argon plasma discharge is studied using 1D-3V particle-in-cell simulations. Calculated electron energy probability functions exhibit three distinct ``temperatures'' for low-, mid-, and high-energy electrons. When compared to published experimental data, the calculated probability functions show a reasonable agreement for the energy range resolved in the measurements (about 2 eV to 10 eV). Discrepancies outside this range lead to differences between computational and experimental values of the electron number density determined from the distribution functions, but the predicted effective electron temperature is within 25\% of experimental values. The impedance of the discharge is interpreted in terms of a homogeneous equivalent circuit model and the driving frequency dependence of the inferred combined sheath thickness is found to obey a known, theoretically-derived, power law. The average power transferred from the field to the electrons (electron heating) is computed, and a region of negative heating near the sheath edge, particularly at higher driving frequencies, is identified. Analysis of the electron momentum equation shows that electron inertia, which would average to zero in a linear regime, is responsible for negative values of power deposition near the sheath edge at high driving frequencies due to the highly nonlinear behavior of the discharge.

physics.plasm-ph↗

arXiv2022

Physical Regimes of Electrostatic Wave-Wave nonlinear interactions generated by an Electron Beam Propagating in a Background Plasma

Electron-beam plasma interaction has long been a topic of great interest. Despite the success of Quasi-Linear (QL) theory and Weak Turbulence (WT) theory, their validities are limited by the requirement of sufficiently dense mode spectrum and small wave amplitude. In this paper, we extensively studied the collective processes of a mono-energetic electron beam emitted from a thermionic cathode propagating through a cold plasma by performing a large number of high resolution two-dimensional (2D) particle-in-cell (PIC) simulations and using analytical theories. We confirm that the initial stage of two-stream instability is saturated due to well-known wave-trapping mechanism. Further evolution occurs due to strong wave-wave nonlinear processes. We show that the beam-plasma interaction can be classified into four different physical regimes in the parameter space for the plasma and beam parameters. The differences between the different regimes are analyzed in detail. For the first time, we identified a new regime in strong Langmuir turbulence featured by what we call Electron Modulational Instability (EMI) that could create a local Langmuir wave packet growing faster than the ion plasma frequency. Ions do not have time to respond to EMI in the initial growing stage. On a longer timescale, the action of the ponderomotive force produces very strong ion density perturbations, and eventually the beam-plasma wave interaction stops being resonant due to strong ion density perturbations. Consequently, in this EMI regime, electron beam-plasma interaction occurs in a periodic (intermittent) process. The beams are strongly scattered by waves, and the Langmuir wave spectrum is significantly broadened, which in turn gives rise to strong heating of bulk electrons. A resulting kappa distribution and a wave-energy spectrum, E^2 (k)~k^(-5), are observed in the strong turbulent regime.

physics.plasm-ph↗

arXiv2022

Electron Modulational Instability in the Strong Turbulent Regime for an Electron Beam Propagating in Background Plasma

We study collective processes for an electron beam propagating through a background plasma using simulations and analytical theory. A new regime where the instability of a Langmuir wave packet can grow locally much faster than ion frequency is clearly identified. The key feature of this new regime is an Electron Modulational Instability that rapidly creates a local Langmuir wave packet, which in its turn produces local charge separation and strong ion density perturbations because of the action of the ponderomotive force, such that the beam-plasma wave interaction stops being resonant. Three evolution stages of the process and observed periodic burst features are discussed. Different physical regimes in the plasma and beam parameter space are demonstrated for the first time.

physics.plasm-ph↗

arXiv2022

Investigating the effects of electron bounce-cyclotron resonance on plasma dynamics in capacitive discharges operated in the presence of a weak transverse magnetic field

Recently, S Patil et al. have reported the existence of an enhanced operating regime when a low-pressure (5 mTorr) capacitively coupled discharge (CCP) is driven by a very high radio-frequency (60 MHz) source in the presence of a weak external magnetic field applied parallel to its electrodes. Their Particle-in-Cell (PIC) simulations show, that a significantly higher bulk plasma density and ion flux can be achieved at the electrode when the electron cyclotron frequency equals half of the applied RF frequency for a given fixed voltage. In the present work we take a detailed look at this phenomenon and further delineate the effect of this "electron bounce cyclotron resonance (EBCR)" on the electron and ion dynamics of the system. We find that the ionization collision rate and stochastic heating is maximum under resonance condition. The electron energy distribution function also indicates that the population of tail end electrons is highest for the case where EBCR is maximum. Formation of electric field transients in the bulk plasma region are also seen at lower values of applied magnetic field. Finally, we demonstrate that the EBCR induced effect is a low pressure phenomenon and weakens as the neutral gas pressure increases. The potential utility of this effect to advance the operational performance of CCP devices for industrial purposes is discussed.

physics.plasm-ph↗

arXiv2018

Spatial symmetry breaking in single-frequency CCP discharge with transverse magnetic field

An independent control of the flux and energy of ions impacting on an object immersed in a plasma is often desirable for many industrial processes such as microelectronics manufacturing. We demonstrate that a simultaneous control of these quantities is possible by a suitable choice of a static magnetic field applied parallel to the plane electrodes in a standard single frequency capacitively coupled plasma device. Our particle-in-cell simulations show a 60% reduction in the sheath width (that improves control of ion energy) and a four fold increase in the ion flux at the electrode as a consequence of the altered ion and electron dynamics due to the ambient magnetic field. A detailed analysis of the particle dynamics is presented and the optimized operating parameters of the device are discussed. The present technique offers a simple and attractive alternative to conventional dual frequency based devices that often suffer from undesirable limitations arising from frequency coupling and electromagnetic effects.

physics.plasm-ph↗

arXiv2017

Validation and benchmarking of two particle-in-cell codes for a glow discharge

The two particle-in-cell codes EDIPIC and LSP are benchmarked and validated for a parallel-plate glow discharge in helium, in which the axial electric field had been carefully measured, primarily to investigate and improve the fidelity of their collision models. The scattering anisotropy of electron-impact ionization, as well as the value of the secondary-electron emission yield, are not well known in this case. The experimental uncertainty for the emission yield corresponds to a factor of two variation in the cathode current. If the emission yield is tuned to make the cathode current computed by each code match the experiment, the computed electric fields are in excellent agreement with each other, and within about 10\% of the experimental value. The non-monotonic variation of the width of the cathode fall with the applied voltage seen in the experiment is reproduced by both codes. The electron temperature in the negative glow is within experimental error bars for both codes, but the density of slow trapped electrons is underestimated. A more detailed code comparison done for several synthetic cases of electron-beam injection into helium gas shows that the codes are in excellent agreement for ionization rate, as well as for elastic and excitation collisions with isotropic scattering pattern. The remaining significant discrepancies between the two codes are due to differences in their electron binary-collision models, and for anisotropic scattering due to elastic and excitation collisions.

physics.plasm-ph↗