Analytic model of power deposition in inductively coupled plasma sources

Abstract

A simple analytic model valid for all collisionality regimes is developed to describe the power deposition in a cylindrical inductively coupled plasma source with a planar coil. The heating is ohmic at high pressures and remains finite at low pressures. The low-pressure collisionless heating is due to kinetic nonlocal effects. The model is in good agreement with other calculations of collisionless heating. A diffusion model is then used to determine the plasma density profile and the electron temperature in terms of the gas pressure and the source geometry. The heating and diffusion models are used to determine the scaling of the inductive electric field with applied frequency and input power, and the results are compared with published experimental data to verify the scaling.

Revisiting the Anomalous rf Field Penetration into a Warm Plasma

“…The electric field profile and the current profile are coupled to each other by Eq. (36). Therefore, the main part of the current and the electric field should decay on distances of order δ a , see Fig.…”

“…(47) by an exponential profile E 0 exp(−x/δ e ) with some fitting procedure for δ e [36][37][38]. By doing so, the property of the electric field in the limit of anomalous skin effect in Eq.…”

“…The real part of the impedance can be calculated by computing the power dissipated by electrons from the skin layer [36] …”

Semi-analytical modeling of the NIO1 source

“…H + 2 in the the case of a hydrogen plasma. The hypothesis of a single ion species is generally not true, especially in molecular gases, but this approximation, also made in previous works [1] is kept in order to simplify the problem. The gas pressure and temperature are considered as external parameters (in particular p gas = 1 Pa and T gas = 400 K unless otherwise stated), thus defining the gas density; the ion temperature is taken equal to the neutral gas temperature, T ion = T gas [2].…”

A self-consistent analytical model for non-collisional heating

“…Non-collisional heating is an important electromagnetic phenomenon in low-pressure inductively coupled plasmas (ICPs) as used in industrial applications such as plasma materials processing [1][2][3][4][5][6]. It has been proposed that non-collisional heating occurs when warm electrons gain net energy while they traverse regions of inhomogeneous electric fields.…”