Rapid calculation of the ion energy distribution on a plasma electrode

Diomede, P.; Economou, Demetre J.; Donnelly, Vincent M.

doi:10.1063/1.4728997

Cited by 10 publications

(17 citation statements)

References 29 publications

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“…Furthermore, the ion energy can be affected by the collisions in the sheath, which broadens the IED [30,48]. In practice, measurement with RFEA can also broaden the IED due to the scattering of ions on the RFEA's grids [30,43]. These broadening effect is equivalent to a normally distributed noise defined by…”

Section: Methodsmentioning

confidence: 99%

Equivalent electric circuit model of accurate ion energy control with tailored waveform biasing

Lemmen

Vermulst

et al. 2022

Plasma Sources Sci. Technol.

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For atomic scale plasma processing involving precise, (an)isotropic and selective etching and deposition, it is required to precisely control the energy of the plasma ions. Tailored waveforms have been employed to bias the substrate table to accurately control this ion energy. Recent research has shown that switched-mode power converters can be used to generate this kind of waveform, with the benefit of increased energy efficiency and flexibility compared to the traditionally used linear amplifiers. In this article, an improved equivalent electric circuit model of the plasma reactor is proposed to allow simulation and bias waveform optimization. The equivalent circuit is analysed for different process phases, including the charge, discharge and post-discharge phase. The proposed model is suitable for electric circuit simulation and can be used for predicting the electric waveforms and ion energy distribution. Plasma parameters are required as input for the model, thus an empirical parameter identification method based on the electric measurements of the bias voltage and output current waveforms is introduced. Since these electrical measurements do not interact with the plasma process, the proposed parameter identification method is nonintrusive. Experiments have been carried out, which demonstrate that the proposed model and parameter identification method provide the expected accuracy.

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Section: Methodsmentioning

confidence: 99%

Equivalent electric circuit model of accurate ion energy control with tailored waveform biasing

Lemmen

Vermulst

et al. 2022

Plasma Sources Sci. Technol.

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“…The time between collisions is determined by pressure. In the case of a wide collisionless plasma sheath (low pressure and low plasma density), simple analytical equations can be applied to obtain a relation between the external parameters of the rf discharge and the IED shape [5,[17][18][19][20][21][22][23][24][25][26]. Some previously developed methods for fast IED calculation [5,26] only take into account the collisionless ion motion.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of a wide collisionless plasma sheath (low pressure and low plasma density), simple analytical equations can be applied to obtain a relation between the external parameters of the rf discharge and the IED shape [5,[17][18][19][20][21][22][23][24][25][26]. Some previously developed methods for fast IED calculation [5,26] only take into account the collisionless ion motion. In [5], the analytical model uses a linear transfer function to relate the time-varying sheath voltage to the time-varying ion energy response at the electrode surface.…”

Section: Introductionmentioning

confidence: 99%

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‘Virtual IED sensor’ for df rf CCP discharges

Bogdanova¹,

Lopaev²,

Рахимова³

et al. 2021

Plasma Sources Sci. Technol.

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Ion-assisted surface processes are the basis of modern plasma processing. Ion energy distribution (IED) control is critical for precise material modification, especially in atomic-level technologies such as atomic layer etching. Since this control should be done in "real time", it requires "real-time" feedback using fast process sensors. In the general case of an industrial plasma reactor, when direct IED measurement is not possible, the IED can be estimated using the concept of a "virtual IED sensor". In this paper, a similar "virtual IED sensor" is considered using an asymmetric dual-frequency (df) rf CCP discharge as an example. It is based on a fast calculation method of the IED at an rf-biased electrode. This approach uses the experimentally measured sheath voltage waveform and plasma density (or ion flux) as input data, and also includes Monte-Carlo simulation of ion motion in the sheath to take into account the effect of ion-neutral collisions. To validate this approach, experiments were carried out using various plasma diagnostics in several gases: argon and xenon as examples of plasma with atomic ions and nitrogen as an example of plasma with molecular ions. It is shown that in all cases it is possible to obtain an adequate IED estimation, close to the experimental one, in a reasonably short time ( tens of seconds when using a modern PC). The results obtained demonstrate the possibility of using a virtual IED sensor in real plasma processing.So, on the one hand, modern plasma processing requires the development of new plasma approaches and systems to ensure an appropriate level of control. On the other hand, this control requires the development of fast sensors.The dual-frequency (df) rf ICP and CCP discharges are widely used today in plasma surface treatment. The simultaneous use of high-frequency and low-frequency rf voltages is aimed at realizing separate control of ion flux and energy. This idea was presented in the works of Goto in the early 1990s [1,2]. Since then, these discharges have been extensively studied both experimentally and theoretically [3,4]. However, one of the main results of these studies is that the two frequencies are generally coupled and the desired functional separate control can only be achieved over a limited range of discharge parameters (frequencies, pressures, and input powers).The multi-frequency discharge excitation was also investigated [5] to reveal the role of the third frequency in controlling the IED shape [6]. In order to better control the ion energy, some new methods of rf discharge excitation have recently been developed. One of them is the excitation of a symmetric rf CCP discharge with two frequencies (the fundamental frequency and its second harmonic) with a phase shift between them. In this configuration, the dc self-bias voltage appears due to the electrical asymmetry effect (EAE) [7]. This voltage is adjusted by the phase shift value between the two frequencies and is used for additional control of ion energy. This idea was further developed in the so-call...

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“…Dai et al [19] and Barnat and Lu [20] presented a self-consistent fluid model which included all time-dependent terms in the ion fluid equations for pulsed dc bias. Diomede et al [21] developed a model allowing rapid calculation of the IEDs on an electrode immersed in plasma for given voltage waveform applied to the electrode through a blocking capacitor. The model combined an equivalent circuit representation of the system with an equation for a damped sheath potential to which ions respond.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of RF Pulsing Effect on Ion Energy Distributions at RF-biased Electrodes

Kwon¹,

Song²,

Yoon³

2014

Applied Science and Convergence Technology

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The ion energy distributions (IEDs) arriving at a substrate strongly affect the etching rates in plasma etching processes. In order to determine the IEDs accurately, it is important to obtain the characteristics of radio frequency (rf) sheath at pulsed rf substrates. However, very few studies have been conducted to investigate pulsing effect on IEDs at multiple rf driven electrodes. Therefore, in this work, we extended previous one-dimensional dynamics model for pulsed-bias electrodes. We obtained the IEDs using the developed rf sheath model and observed that numerically solved IEDs are in a good agreement with the experimental results.

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Rapid calculation of the ion energy distribution on a plasma electrode

Cited by 10 publications

References 29 publications

Equivalent electric circuit model of accurate ion energy control with tailored waveform biasing

Equivalent electric circuit model of accurate ion energy control with tailored waveform biasing

‘Virtual IED sensor’ for df rf CCP discharges

Numerical Investigation of RF Pulsing Effect on Ion Energy Distributions at RF-biased Electrodes

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