Characteristics of anomalous skin effect and evolution of power absorption regions in a cylindrical radio frequency inductively coupled plasma

Abstract

In a low-pressure radio-frequency (13.56 MHz), inductively coupled argon plasma generated by a normal cylindrical rf coil, electric field, current density, and absorbed power density is calculated from magnetic field measured with a phase-resolved magnetic probe. The anomalous skin effect (ASE) for the cylindrical rf coil is compared to those previously reported for the planar and re-entrant cylindrical rf coils. Physical reasons for our observed characteristics of ASE are presented. With the increasing discharge power, the size and the number of negative and positive power absorption regions evolve into several distinct patterns. For the low discharge power (at 156.9 W), there is one area of positive and one area of negative power absorption in the radial direction. For the medium discharge power (279 W–683.5 W), there are two areas of negative and two areas of positive power absorption. For the even higher discharge power (above 803.5 W), the number of areas is the same as that of the medium discharge power, but the size of the inner positive and negative power absorption areas is approximately doubled and halved, respectively, while the outer positive and negative power absorption areas slightly shrinks. The evolution of positive and negative power absorption regions is explained as a result of electron thermal diffusion and the energy conversion between rf current and electric field. The spatial decays of electric field and current density are also elucidated by linking them with the positive and negative power absorption pattern.

Fundamental study towards a better understanding of low pressure radio-frequency plasmas for industrial applications

“…By solving the Maxwell's equations and the linearized electron Boltzmann's equation, You and Yoon [32] derived the non-local conductivity in the solenoidal ICP, and predicted the anomalous skin effect as well as negative power 085202-6 absorption. These theoretical predictions have been observed in the experiments of the planar [33] and the solenoidal [34] ICPs operated at low pressure. Recently, Yang et al studied the effects of the conductivity during the transition from collisionless to collisional regimes in cylindrical ICPs by a numerical model, which is based on self-consistent coupling of the electron kinetics equation, electromagnetics equation, and global model equations.…”

“…Experimentally determined spatial structures of the harmonics of the magnetic field 085202-17 were compared with simulations based on the nonlinear transmission line model described by Eqs. ( 32)- (34), showing a reasonably good agreement (see Fig. 22).…”

Phase-resolved profiles of electron energy deposition in inductively coupled radio-frequency plasmas driven under confronting divergent magnetic fields

“…This seems similar to experimental results on negative power absorption. 35,37,38) In addition, v θ (t) is always negative in S 38,80 . v θ (t) is dependent on the gradient of n(r, z) in the radial direction as mentioned in Sect.…”

“…[28][29][30][31][32] Some mechanisms of the power deposition to electrons such as anomalous skin effect in ICPs have also been investigated. [33][34][35][36][37][38] However, features of the power deposition specific to the three above-mentioned regions are still unclear from the viewpoint of microscopic electron motion because of the complexity of the electron behavior under non-uniform crossed electric and magnetic fields.…”

A new B-dot probe circuit for magnetic diagnostics of radio frequency discharges

“…[1][2][3][4][5][6][7] Particularly in inductively coupled plasmas (ICP), magnetic field measurements allow visualization of the spatial distribution of radio frequency (rf) current density, electric field as well as power deposition in the reactor, providing insights into important physics, such as the anomalous skin effect. 8,9 On the other hand, accurate measurements of the magnetic field in capacitively coupled plasmas (CCP) are challenging because of the inherently weak magnetic field, and the so-called capacitive pickup, 10 which stems from the capacitive coupling between the oscillating plasma potential and the probe coil, causing serious interference.…”