Dynamic investigation of mode transition in inductively coupled plasma with a hybrid model

Abstract

Industrial inductively coupled plasma (ICP) sources are always operated in low gas pressure 10–100 mTorr, therefore in order to accurately investigate the mode transition of ICP, we developed our pure fluid model (2009 J. Appl. Phys. 105 083306) into a hybrid fluid/Monte Carlo (MC) model, where the MC part is exploited to take in more dynamic characteristics of electrons and self-consistently calculate the rate coefficients and electron temperature used in the fluid module, and more crucially to study the electron energy distribution function (EEDF) evolution with mode transition. Due to the introduction of the nonlocal property of the electrons at relatively low pressures, the dependences of the plasma density on the coil current, including the mode transitions, are distinctly different at low and high pressures when simulated by this improved hybrid model (HM), while the trends for different pressures obtained from the original pure fluid model (PFM) are the same in all cases. Furthermore, the computed peaks of the electron density profile by the HM shift from the discharge centre in the E mode to the intense inductive field heating area (about half of the radius of the reaction chamber under the dielectric window) in H mode. In addition, the electron temperature profiles of two modes under different pressures simulated by HM are totally higher than the results of PFM. When the pressure is low, there is a minimum exhibited in the bulk plasma of the electron temperature profiles of the E mode, and along with the mode transition the distribution area of low temperature is substantially reduced. Moreover, this phenomenon disappears when the gas pressure is increased. Accompanied by this, the calculated EEDF of the E mode in the low pressure also demonstrates an absolutely dominant low energy electron fraction (about ⩽5 eV); while transforming to the H discharge most of the electrons carry an energy of 1–10 eV. The tendencies of the calculated EEDF evolution with mode transition under relatively high pressures agree well with the experimental measurements of EEDF of Lee et al (2009 Appl. Phys. Lett. 90 191502), but the determination mechanisms are still in dispute and require further examination.

E-H heating mode transition in inductive discharges with different antenna sizes

“…[10][11][12][13][21][22][23][24][25][26][27][28][29][30] Theoretical studies have been conducted, as follows. Kortshagen et al 31 calculated the critical antenna current to achieve a stable H mode.…”

Mode Transition and Hysteresis in Inductively Coupled Plasma Sources

“…In this part, the characteristics of electron parameters, density, temperature and energy distribution function and plasma potential at two modes are presented via the two-dimensional hybrid model [14]. The hybrid model consists of three parts, that is, fluid module, electron Monte Carlo module and electromagnetic module.…”

Dependence of E-H transition in argon ICP discharges for treatment of organic molecules

“…, while H-mode ranges from 10 10 to 10 11 cm -3 at the same applied power [8,10,11]; the plasma potential is reduced at the H-mode even with the increase of applied power [12,13]; the EEDF changes to a more Maxwellian electron distribution at the Hmode [9,10,14]; electron temperature is reduced at H-mode, while gas temperature is increased [13][14][15]; electron-electron collision frequency is greatly increased [12]; after the H-mode is initiated, it can be sustained even at lower powers [12,16]; finally, both E and H modes can coexist inside the reactor [9].…”

“…At higher powers, an inductive mode becomes relevant, generating plasma due to an electromagnetic field from the same coil, called as H-mode. Often, these discharges are generated by E-mode and the transition can occur by increasing the applied power, which is visible by a sudden increase on discharge brightness size and density [7][8][9]. Several studies already evaluated the changes that occur in plasma properties during this transition and some of the most relevant results are as follows: E-mode has an electron density generally close to 10 9 cm -3…”