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

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.