Driving frequency effect on discharge parameters and higher harmonic generation in capacitive discharges at constant power densities

Abstract

Very high frequency (VHF) driven capacitive discharges are now being increasingly adopted for plasma-based materials processing due to their high processing rates and lower substrate damage. Past studies related to complex plasma dynamics and higher harmonics generation in such systems were limited to constant voltage/current conditions, whereas, industrial systems are mostly driven by constant power density sources. In the present study, using particle-in-cell (PIC) simulation, we explore the dynamics of collisionless symmetric capacitive discharges that is operated at constant power densities. Our focus is on the effect of the driving frequency on the discharge parameters like the electron density/temperature, the electron energy distribution function (EEDF), the ion energy distribution function (IEDF), and the generation of higher harmonics in the device. The simulations are performed for a driving frequency from 27.12 to 100 MHz in argon plasma at a gas pressure of 1 Pa and for two values of the power density, namely, 2 kW m−3 and 20 kW m−3. It is observed that the required discharge voltage for maintaining constant power density decreases and discharge current increases with an increase in the driving frequency. A transition frequency is observed at both power densities. The density decreases (electron temperature increases) before the transition frequency and the trend is reversed after crossing the transition frequency. The EEDF shows an enhancement in the population of the mid-energy range of electrons as the driving frequency increases up to the transition frequency thereby changing the shape of EEDF from bi-Maxwellian to nearly Maxwellian, and then transforms into a nearly bi-Maxwellian at higher driving frequencies. The IEDF at the electrode surface shows bimodal behaviour at a lower driving frequency, becoming more pronounced at a power density of 20 kW m−3, and then turning into a single energy peak. The corresponding maximum ion energy is found to decrease with driving frequency.

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

“…During these interactions, the instantaneous sheath edge position is modulated with highfrequency oscillations. Similar effects have been observed in capacitive discharges operating at a very high frequency [9][10][13][14]70]. These multiple ionization beams support higher plasma density in the discharge that is observed at N = 12.…”

“…As shown in figure 9, the energy spread in the bi-modal energy peaks (E) is decreasing with an increase in the value of N. For the current chosen range (N = 2 -12), the value of E is decreased from 34 eV to 17 eV i.e., a 50% drop in the energy spread is observed. A decrease in the value of E is on the one hand due to an increase of high-frequency content in the driving waveform that drives IEDF from a bi-modal shape to a narrow distribution as observed in the very high frequency CCP discharges [10]. The high-frequency component on the instantaneous sheath edge position is clearly observed as shown in figure 6 (d).…”

“…In this work, we adapted the particle-in-cell (PIC) simulation method along with the Monte Carlo Collision Scheme [63][64]. The simulation is performed in one spatial dimension and 3 velocity dimensions (1D3V) using a well-tested and benchmarked code [72] which has been widely used in literature for capacitive discharges [9][10][13][14][15][65][66][67][68][69][70][71]. This code can handle both current and voltage-driven modes and we have used the earlier one for all sets of simulations.…”

“…For optimizing the plasma processes, control of vital parameters such as ion energy and ion flux is highly desired. In a single-frequency operated CCP discharge this is often challenging as the power deposited into both electrons and ions varies with the RF waveform current/ voltage amplitude [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. CCP operated using dual-frequency (DF) waveforms provides a level of independent control over ion energy and flux [18][19][20][21][22][23][24][25][26][27][28][29].…”

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

“…For the present study, we have used a well-tested and benchmarked 1D3V, electrostatic, selfconsistent, PIC code 32,33 . The code has been used extensively in previous studies and details can be found in the literatures [34][35][36][37][38][39][40][41][42][43][44][45][46] . As an input, a current waveform is chosen given by the following mathematical expression:…”