A model for tailored-waveform radiofrequency sheaths

This paper is the first from a set of two companion papers on radio-frequency (RF) discharges. These two papers are in turn part of a larger series on the foundations of plasma and discharge physics. In this part we cover the basics of non-magnetized capacitive and inductive RF discharges, introduce the main concepts related to them and provide reference literature for further reading. In the second part we concentrate on RF discharges in the presence of external magnetic field. These types of RF discharges find a wide range of applications in various industries. Among the most prominent examples are the microelectronics industry for etching and deposition of thin films, the medical and food industry for the application of various coatings and changing the wettability of surfaces, the space industry to power ion-gridded thrusters for satellites, the fusion and elementary particle research for the production of beams of energetic ions or atoms. The paper introduces the basic concepts of RF power deposition and describes in more detail the operating conditions of the plasma reactors. The most important physical phenomena encountered in these discharges are outlined through the use of simplified models. The paper is intended as an entry point for newcomers to the field and provides ample of references (including textbooks) for further reading on the more specific and/or subtle aspects of the operation of these types of RF discharges.

Section: The Rf Sheathmentioning

confidence: 99%

Section: The Electromagnetic Regimementioning

confidence: 99%

Foundations of capacitive and inductive radio-frequency discharges

Chabert¹,

Tsankov²,

Czarnetzki³

2021

“…Several analytical sheath models for both the single and dual frequency CCP have been developed since Lieberman's early pioneering work [22]. A good overview of these works can be found in [23][24][25]. In most of the analytical works mentioned above, the solutions are only possible when the time derivative terms in the fluid equations are neglected.…”

Section: Analytical Modelmentioning

confidence: 99%

“…Due to the nonlinear interactions between the two sources, the characteristics of the 2f CCP sheath are much more complex than the single frequency CCP. Different analytical sheath models based on various assumptions [11,[22][23][24][25] and particle in cell/ Monte Carlo codes (PIC/MCCs) [18,19] are now available to study the complex coupling between the two sources that leads to the separate control of ion flux and ion energy in 2f CCPs. Here, we have preferred a current driven analytical approach over the PIC/MCCs to study the relation between the instantaneous sheath potential and plasma parameters.…”

Section: Introductionmentioning

confidence: 99%

Study of dual radio frequency capacitively coupled plasma: an analytical treatment matched to an experiment

Saikia

Bhuyan

Escalona

et al. 2018

The behavior of a dual frequency capacitively coupled plasma (2f CCP) driven by 2.26 and 13.56 MHz radio frequency (rf) source is investigated using an approach that integrates a theoretical model and experimental data. The basis of the theoretical analysis is a time dependent dual frequency analytical sheath model that casts the relation between the instantaneous sheath potential and plasma parameters. The parameters used in the model are obtained by operating the 2f CCP experiment (2.26 MHz+13.56 MHz) in argon at a working pressure of 50 mTorr. Experimentally measured plasma parameters such as the electron density, electron temperature, as well as the rf current density ratios are the inputs of the theoretical model. Subsequently, a convenient analytical solution for the output sheath potential and sheath thickness was derived. A comparison of the present numerical results is done with the results obtained in another 2f CCP experiment conducted by Semmler et al (2007 Plasma Sources Sci. Technol. 16 839). A good quantitative correspondence is obtained. The numerical solution shows the variation of sheath potential with the low and high frequency (HF) rf powers. In the low pressure plasma, the sheath potential is a qualitative measure of DC self-bias which in turn determines the ion energy. Thus, using this analytical model, the measured values of the DC self-bias as a function of low and HF rf powers are explained in detail.

“…Mussenbrock et al [10] reported a nonlinear global model for DF CCP. Chabert and Turner [11] proposed even a model for arbitrary RF voltages. Czarnetzki developed an analytical model that is applicable for the full range from collisionless to fully collisional sheaths [12].…”

Section: Introductionmentioning

confidence: 99%

Analytical plasma impedance model of dual frequency capacitive discharges with ion dynamics

Kuhfeld¹,

Sakiyama²,

Czarnetzki³

2019

Based on a fluid simulation, an analytical equivalent circuit model was developed for collisional plasmas with dual frequency (DF) excitation. Primary focus is on a fully collisional sheath and a low frequency (LF) below the ion plasma frequency. In the analytical model, the high frequency (HF) component is expressed as a series RC circuit, which matches the classical result for the limit of single frequency radio frequency discharges. The LF circuit is expressed as a parallel RC circuit to consider the response of ions to the LF voltage. The model requires three main parameters: the magnitudes of the HF and LF voltages, which are known during discharge operation and the space and time averaged ion density, which is in general unknown and needs to be determined by other means. Explicit formulas for the calculation of the HF and LF impedances are provided. Good agreement is found between the new analytical model and the fluid simulation. It is worth noting that previously published analytical models fail to reproduce the impedances, predominantly because the dynamic ion behavior and the parallel nature of the resulting ion current in respect to the LF displacement current are not considered. A practical application of the model is the calculation of the ion density in the discharge from measured impedances. For this purpose both the LF and the HF impedances can be used. A comparison of the densities estimated from the different impedances and the average density in the simulation show again good agreement.