Harmonic content of electron-impact source functions in inductively coupled plasmas using an “on-the-fly” Monte Carlo technique

Electron temperatures in low-pressure (<10s mTorr) inductively coupled plasma (ICP) reactors operating at 10s MHz do not significantly vary during the radio frequency (rf) cycle. There can be, however, considerable modulation of electron-impact source functions having high-threshold energies due to modulation of the tail of the electron energy distributions (EEDs). In many instances, it is convenient to use cycle-averaged values for these quantities in models due to the computational burden of computing and storing spatial and time-dependent EEDs. In this paper an “on-the-fly” (OTF) Monte Carlo technique is described to address these time-dependent plasma parameters. The OTF method directly computes moments of the EEDs during advancement of the trajectories of the pseudoparticles, thereby reducing computational complexities. The method can also be used to directly calculate the harmonic components of excitation, which can subsequently be used to reconstruct the time-dependent source functions. The OTF technique was incorporated into a two-dimensional plasma equipment model to investigate the time dependence of electron-impact source functions in low-pressure ICP systems. We found that even harmonics dominated the source functions for high-threshold processes, and that the harmonic content decreased with increasing frequency and increased with increasing pressure. We also observed axial pulses of excitation and increasing harmonic content at low pressures which are attributed to nonlinear Lorentz force acceleration and nonlocal transport.