Particle-In-cell simulations of nonlocal and nonlinear effects in inductively coupled plasmas

Abstract

The kinetic effects in an inductively coupled plasma (ICP) due to thermal motion of particles modified by self-consistent magnetic fields are studied by using a particle-in-cell (PIC) simulation. In the low pressure, low frequency regime, electron mean free paths are large relative to device size and the trajectories are strongly curved by the induced radio frequency (RF) magnetic field. This causes problems for linear theories, which ignore the influence of the magnetic field on the particles, and are therefore unable to recover effects accumulated along each nonlinear path.The tools to perform high-performance parallel PIC simulations of inductively coupled plasmas were developed to allow rapid scanning of a broad range of the input parameters, such as wave amplitude, frequency, and plasma temperature. Different behavioural regimes are identified by observing the resultant variations in the skin depth, surface impedance, and ponderomotive force (PMF). At low electron-neutral collision rates, these are shown to include the local collisionless regime, the anomalous skin effect regime, and the nonlinear regime.The local collisionless regime occurs at high driving frequencies and is characterized by plasma behaviour independent of both the driving frequency and amplitude: a short skin depth, low energy absorption, and strong PMF. The anomalous skin effect regime occurs at low frequencies and low amplitudes: the plasma varies with driving frequency, but not driving amplitude, the skin depth increases with frequency, the plasma is much more absorptive in the anomalous regime than in the local regime, and the PMF increases with frequency. The nonlinear regime occurs at low frequencies and high amplitudes: the plasma varies with driving amplitude, but not frequency, the skin depth decreases with amplitude, there is low energy absorption, and the PMF increases with wave amplitude.The simulation runs in four modes: linear collisionless, linear collisional, nonlinear collisionless, and nonlinear collisional. The linear modes, in which the particles ignore the magnetic field, are used to validate the results against theory, while the nonlinear modes are used to test actual plasma behaviour. In linear collisionless mode, the plasma was found to exhibit only the local collisionless and anomalous skin effect regimes, as expected by theories. In nonlinear collisionless mode, the plasma exhibits the nonlinear regime in addition to the regimes found in linear mode. Finally, the nonlinear regime disappears in nonlinear collisionless mode because the curved paths caused by the magnetic field are disrupted by collisions.Finally, the regime boundaries are investigated as a function of temperature. Since the plasma properties vary continuously, a boundary exists where two regimes share the same characteristics. From linear theories, it is known that the division between the local collisionless and anomalous skin effect regimes moves to higher frequencies as the plasma temperature is increased. When nonlinear fields are present, this still occurs, but in conjunction with the boundary between the local collisionless and nonlinear regimes moving to higher wave amplitudes. Temperature also effects the boundary between the anomalous skin effect and nonlinear regimes, causing the minimum frequency of the anomalous skin effect regime to be reduced at low wave amplitudes.