Resonant sheath heating in weakly magnetized capacitively coupled plasmas due to electron-cyclotron motion

An electron heating mechanism based on a resonance between the cyclotron motion of electrons and the radio frequency sheath oscillations is reported in weakly magnetized capacitively coupled plasmas at low pressure. If half of the electron cyclotron period coincides with the radio frequency period, then electrons will coherently collide with the expanding sheath and gain substantial energy, which enhances the plasma density. A relation between the magnetic field and the driving frequency is found to characterize this resonance effect and the kinetics of electrons are revealed at resonance conditions for various driving frequencies.

Figure 1

Schematic plot of the magnetized rf CCP experimental setup.

Figure 2

Schematic plot of the simulation setup for a magnetized rf CCP.

Figure 3

Space- and time-averaged plasma density (unit in ${10}^{15}{\mathrm{m}}^{-3}$) as a function of the transverse magnetic fields for different frequencies and electrode gaps resulting from PIC simulations at 0.1 Pa (a) and 1.5 Pa (c) for a driving voltage amplitude of 300 V. (b) Externally applied magnetic field at which the highest plasma density is found as a function of the driving frequency obtained from (a) (red points) and from the resonance relation $0.5T_{\mathrm{ce}}=T_{\mathrm{rf}}$ (solid line). (d) Peak density from experiment at 4-cm gap with 20-W power input, and from PIC simulations for two different electrode gaps of 4 cm with 180-V applied voltage amplitude and 7 cm with 300-V applied voltage amplitudes for 40 MHz at 0.16 Pa.

Figure 4

Position of a typical bouncing electron and of the sheath edge, and the electron kinetic energy as a function of time at (a) 13.56 MHz and (c) 60 MHz. Temporal evolution of the resonance in the electron $x-v_x$ (unit in ${10}^6\mathrm{m}/\mathrm{s}$) phase space at (b) 13.56 MHz and (d) 60 MHz. $S_{\max }$ are the maximum sheath width.

Figure 5

Spatiotemporal evolution of the electron impact ionization rate (unit in ${10}^{21}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$) at 60 MHz (contours). The sheath edges are indicated by white lines within two consecutive rf periods.

Figure 6

Time-averaged density (unit in ${10}^{13}{\mathrm{m}}^{-3}$) profiles of high energy electrons ($\ge$ 30 eV) for different transverse magnetic fields, driving frequencies and electrode gaps: (a) 13.56 MHz at 11 cm, (b) 27.12 MHz at 11 cm, (c) 45 MHz at 7.5 cm, and (d) 60 MHz at 7.5 cm.