Kinetic interpretation of resonance phenomena in low pressure capacitively coupled radio frequency plasmas

Abstract

The kinetic origin of resonance phenomena in capacitively coupled radio frequency plasmas is discovered based on particle-based numerical simulations. The analysis of the spatio-temporal distributions of plasma parameters such as the densities of hot and cold electrons, as well as the conduction and displacement currents reveals the mechanism of the formation of multiple electron beams during sheath expansion. The interplay between highly energetic beam electrons and low energetic bulk electrons is identified as the physical origin of the excitation of harmonics in the current.Capacitively coupled radio frequency (CCRF) discharges are indispensable tools for semiconductor manufacturing and other innovative applications [1,2]. At the same time, they are challenging physical systems due to their complex and nonlinear dynamics. At low neutral gas pressures of a few Pa or less, CCRF discharges are operated in a strongly non-local regime. In the so-called "α-mode", electron heating is dominated by stochastic sheath expansion heating [3] and electric field reversal during sheath collapse [4][5][6][7]. Stochastic heating was modelled extensively in the past in the frame of a hard wall model, as well as pressure heating [8][9][10][11][12][13][14][15][16][17]. During the phase of sheath expansion, energetic electron beams are generated and propagate into the plasma bulk, where they sustain the discharge via ionization and lead to a Bi-Maxwellian electron energy distribution function (EEDF) [18][19][20][21][22][23][24]. At low pressures, resonance effects such as the plasma series resonance (PSR) [27][28][29][30] and the plasma parallel resonance (PPR) [31][32][33] can be self-excited and strongly enhance the electron heating [19,29]. In the presence of a sinusoidal driving voltage waveform, the excitation of the PSR results in a non-sinusoidal RF current, due to the appearance of harmonics of the driving frequency [30]. Although these have been observed in experiments [21], they are usually neglected in most models of electron heating in CCRF plasmas. Existing theories which include resonance effects are zero-dimensional global models based on equivalent electrical circuits [29] as well as spatially resolved models based on the cold plasma approximation [30]. As these models do not include any kinetic effects, such resonances should be investigated on a microscopic kinetic level. A kinetic interpretation is required to clarify some of the most important open questions about electron heating dynamics in CCRF plasmas: What is the kinetic origin of the generation of high frequency (HF) oscillations of the RF current and the generation of multiple electron beams during one phase of sheath expansion such as observed in previous works [37]? In what way is current continuity (∇ · j tot = 0) ensured at all times within the RF period in the presence of electron beams, where the total current density j tot = j d + j c is decomposed into the displacement and conduction current density? Our aim is to provide access to a kinetic inter...

The role of surface quenching of the singlet delta molecule in a capacitively coupled oxygen discharge

“…High frequency oscillations in the electron power absorption density adjacent to the expanding sheath edge are seen at 25 and 50 mTorr and become more clear as the pressure is increased and the surface quenching coefficient is decreased. These oscillations are a beam-plasma instability at the electron plasma frequency, due to an electron-electron two-stream instability between the bulk electrons and electrons accelerated by the moving sheath [11,64].…”

“…This electron heating process is referred to as * tumi@hi.is electron bounce resonance heating (BRH) and can occur for certain combinations of driving frequency and electrode gap [3][4][5][6][7]. The sheath motion and thus the stochastic heating can also be enhanced by self-excited non-linear plasma series resonance (PSR) oscillations [8][9][10][11]. Collisionless electron heating via sheath oscillations is commonly referred to as the α-mode [12].…”

Disparity between current and voltage driven capacitively coupled radio frequency discharges

“…Figures 6(c) and (d) show the corresponding spatially averaged ionization rate, R ion , as a function of time. In the voltage driven scenario (b), multiple electron beams [14,16,20] are accelerated during the whole phase of sheath expansion. This generation of fast electrons is related to the electron power gain P 1 at the sheath edge shown in figure 5(b).…”

“…These energetic electrons are accelerated by the expanding sheath, penetrate into the plasma bulk and assist to sustain the discharge via efficient ionization. In a voltage driven system, they can create an electric field reversal between the plasma sheath and the bulk, which attracts cold bulk electrons back towards the expanding sheath [18][19][20]. These bulk electrons react on the timescale of the local plasma frequency and their nonlinear interaction with the sheath leads to significant oscillations in the RF current, while the RF voltage almost sinusoidal.…”

On electron heating in a low pressure capacitively coupled oxygen discharge

“…This effect is referred to as electron bounce resonance heating (BRH) [3]. The sheath motion and thus the stochastic heating can also be enhanced by selfexcited non-linear plasma series resonance (PSR) oscil- * tumi@hi.is lations [4][5][6][7][8]. At higher pressures some of the power is deposited by ohmic heating in the bulk plasma due to collisional momentum transfer between the oscillating electrons and the neutrals.…”