High frequency sheath modulation and higher harmonic generation in a low pressure very high frequency capacitively coupled plasma excited by sawtooth waveform

Abstract

A particle-in-cell simulation study is performed to investigate the discharge asymmetry, higher harmonic generations and electron heating mechanism in a low pressure capacitively coupled plasma excited by a saw-tooth like current waveform for different driving frequencies; 13.56 MHz, 27.12 MHz, and 54.24 MHz. Two current densities, 50 A m−2 and 100 A m−2 are chosen for a constant gas pressure of 5 mTorr in argon plasma. At a lower driving frequency, high frequency modulations on the instantaneous sheath electric field near to the grounded electrode are observed. These high frequency oscillations create multiple ionization beam like structures near to the sheath edge that drives the plasma density in the discharge and responsible for discharge/ionization asymmetry at lower driving frequency. Conversely, the electrode voltage shows higher harmonics generation at higher driving frequencies and corresponding electric field transients are observed into the bulk plasma. At lower driving frequency, the electron heating is maximum near to the sheath edge followed by electron cooling within plasma bulk, however, alternate heating and cooling i.e. burst like structures are obtained at higher driving frequencies. These results suggest that electron heating in these discharges will not be described accurately by simple analytical models.

Ion energy distribution function in very high frequency capacitive discharges excited by saw-tooth waveform

“…The combination of above 2 effects makes the discharge asymmetric as driving frequency is reduced. Similar results were observed in the case of saw-tooth like current waveform 29 , where a strong asymmetry is observed at 13.56 MHz when compared to 54.24 MHz driving frequency. In addition to the discharge asymmetry, variation in the driving frequency have shown multiple ionization beams that are extended up to the opposite sheath and shown to modify the instantaneous sheath edge positions lead to the excitation of higher harmonics 29 .…”

“…Similar results were observed in the case of saw-tooth like current waveform 29 , where a strong asymmetry is observed at 13.56 MHz when compared to 54.24 MHz driving frequency. In addition to the discharge asymmetry, variation in the driving frequency have shown multiple ionization beams that are extended up to the opposite sheath and shown to modify the instantaneous sheath edge positions lead to the excitation of higher harmonics 29 . The frequency of the sheath modulation is observed to increase with reducing frequency and therefore claimed to be one of the parameters for driving the enhanced plasma density in the discharge at lower fundamental driving frequency of the saw-tooth like waveform.…”

“…One of the examples is multi-harmonic waveforms in which the plasma density and ion flux asymmetry at one electrode increases with the number of harmonics while the average ion energy on the other electrode remains nearly constant [23][24][25][26] . Another way to produce asymmetric plasma response is to use the temporally asymmetric waveforms such as saw-tooth like waveforms [27][28][29] . Such type of asymmetry is known as slope EAE.…”

“…We follow previous studies with the investigation of IEDF in the CCP discharge using an ideal saw-tooth like current waveform at a very high frequency. In our previous work 29 , we focused on the electric field non-linearity and higher harmonics generation in a symmetric CCP. In the present study, we extended our previous study to investigate the effect of current density amplitude on the IEDF at the powered and grounded electrode in a symmetric CCP discharge excited by sawtooth like current waveform at a fundamental driving frequency of 27.12 MHz.…”

Bispectral analysis of nonlinear mixing in a periodically driven Korteweg-de Vries system

“…The presence and evolution of nonlinear modes or disturbances are, in fact, generic to nonlinear media such as cnoidal waves in metamaterials [35], cnoidal-square waveforms of dust acoustic waves [36], and sawtooth-like shock waves [37]. When the driving wave is applied externally, it can also take a variety of waveforms, such as using a cnoidal waveform electrical or optical signals to generate frequency combs in Kerr microresonators [38], use of a sawtooth wave for higher harmonic generation in a plasma [39] and the use of cnoidal waves to generate nonlinear frequency combs in microring resonators [40]. The present work is aimed at studying the impact of such waveforms on the nonlinear mixing phenomena in plasmas.…”