Fluid Simulations Of Nonlinear Effects In Inductively Coupled Plasma

Inductively coupled plasma (ICP) is an important plasma source in the fields of semiconductor fabrication, due to its advantages at low pressures. Low frequency and low pressure inductive sources are attracting special interest due to their many advantages, such as high transfer efficiency, and highly uniform and high-density plasma in large volumes. Moreover, many interesting physical phenomena will occur in ICPs operating at low pressure and frequency, such as harmonic effects and E-H mode transition, which are known as the nonlinear effects. These nonlinear effects will influence the process of manufacturing technique. Therefore, it is necessary to investigate the nonlinear effects in ICPs.A fluid model is self-consistently established to investigate the harmonic effects in an inductively coupled plasma, where the electromagnetic field is solved by the finite difference time domain (FDTD) technique. The spatiotemporal distribution of harmonic current density, harmonic potential and other plasma quantities, such as radio-frequency (rf) power deposition, plasma density and electron temperature, has been investigated. Distinct differences in current density have been observed when calculated with and without Lorentz force, which indicates that the nonlinear Lorentz force plays an important role in the harmonic effects, especially at low frequencies. Moreover, the even harmonics are larger than the odd harmonics both in the current density and the potential. Finally, the dependence of various plasma quantities with and without the Lorentz force on various driving frequencies is also examined. It is shown that the deposited power density decreases and the depth of penetration increases slightly because of the Lorentz force. The electron density increases distinctly while the electron temperature remains almost the same when the Lorentz force is taken into account.Moreover, the E-H mode transition of ICP has also been investigated by adjusting the coil current, using the self-consistently model, where the FDTD method is also employed. The capacitive component of absorbed power increases at first, and then decreases when the discharge transfers to H mode. The inductive component of absorbed power increases as the coil current increases. The electron density increases during the whole process of the transition from E mode to H mode. Furthermore, the spatial distributions of rf fields, electron temperature and plasma density during the mode transition are examined. The radial component of the electric field decreases with increasing current. While the axial component of the electric field remains almost the same at first, and then decreases suddenly at the certain value of current. The azimuthal electric field increases during the transition. The amplitude and pattern of the electron temperature change obviously due to the various effects of different fields. The plasma density increases with increasing current, and the position of the peak density moves to the dielectric window.