Multi frequency matching for voltage waveform tailoring

Schmidt, Frederik; Schulze, Julian; Johnson, Erik; Booth, Jean‐Paul; Keil, D.; French, David M.; Trieschmann, Jan; Mussenbrock, Thomas

doi:10.1088/1361-6595/aad2cd

Cited by 37 publications

(35 citation statements)

References 46 publications

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“…Verboncoeur et al [35] implemented a series RLC circuit driven by a current or a voltage source in particle-in-cell/Monte Carlo collision (PIC/MCC) simulations. Schmidt et al [36,37] investigated the coupling of an equivalent circuit plasma model and an electric external circuit composed of lumped elements.…”

Section: Introductionmentioning

confidence: 99%

Disparity between current and voltage driven capacitively coupled radio frequency discharges

Wilczek

Trieschmann

Schulze

et al. 2018

Plasma Sources Sci. Technol.

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In simulation as well as analytical modeling studies of low-pressure capacitively coupled radio frequency (CCRF) discharges, the assumption of both a driving voltage source or a driving current source is commonly used. It is unclear, however, how and to what extent the choice of the mode of driving, that prescribes either a sinusoidal discharge voltage or a sinusoidal discharge current, itself defines the discharge dynamics that results from these studies. To address this issue, 1d3v cylindrical particle-in-cell/Monte Carlo collisions simulations of asymmetric CCRF discharges are performed in the low pressure regime (p<2Pa). We study the nonlocal and nonlinear dynamics of these discharges on a nanosecond timescale. We find that the excitation of the plasma series resonance in the voltage driven case strongly enhances the nonlinear electron power dissipation. However, this resonance is suppressed when a current source is used, because the excitation of harmonics in the RF current is not allowed. Consequently, significant differences between both driving sources are observed in the plasma density as well as in the electron and the power coupling dynamics. We conclude that caution is advised in comparisons between simulations and experiments, as in the former the discharge dynamics is partly defined by the method of driving of the plasma source, while in the latter the addressed resonance phenomena are inherently present at low pressures, since experiments are typically voltage driven.

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Section: Introductionmentioning

confidence: 99%

Disparity between current and voltage driven capacitively coupled radio frequency discharges

Wilczek

Trieschmann

Schulze

et al. 2018

Plasma Sources Sci. Technol.

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“…Note that it is necessary to anticipate variations in the plasma load with plasma conditions, in addition to the reactor characteristics, to choose reasonable values for these elements, as discussed in Ref. 29. In addition, since the load impedance at each frequency is not perfectly known in advance, these reactive components need to be adjustable.…”

Section: B Impedance Matching Networkmentioning

confidence: 99%

“…Recently, the performance of this design was investigated by numerical simulation, using an equivalent plasma circuit model which selfconsistently calculates the electron temperature and plasma density. 29 That work predicted that effective impedance matching can be achieved for plasmas operating over a range of gas pressures and using several excitation frequencies.…”

Section: Introductionmentioning

confidence: 99%

Experimental demonstration of multifrequency impedance matching for tailored voltage waveform plasmas

Wang

Dine²,

Booth

et al. 2019

Journal of Vacuum Science &Amp; Technology A: Vacuum, Surfaces, and Films

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Driving radiofrequency capacitively coupled plasmas by multiharmonic tailored voltage waveforms (TVWs) has been shown to allow considerable control over various plasma properties for surface processing applications. However, industrial adoption of this technology would benefit from more efficient solutions to the challenge of impedance matching the radiofrequency power source to the load simultaneously at multiple harmonic frequencies. The authors report on the design and demonstration of a simple, practical multifrequency matchbox (MFMB) based on a network of LC resonant circuits. The performance of the matchbox was quantified in terms of a range of matchable impedances (when matching a single frequency at a time), as well as for the independence of each match to changes at adjacent harmonics. The effectiveness of the MFMB was demonstrated experimentally on an Ar plasma excited by a three-frequency TVW with a fundamental frequency of 13.56 MHz. Under the plasma conditions studied, the power coupling efficiency (at the generator output) was increased from less than 40% (without impedance matching) to between 80% and 99% for the different exciting frequencies.

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“…The global plasma model utilized in this work is based on considerations introduced and discussed in [4,6,8,17], while its interaction with an external electric circuit has been studied using ngSPICE [18] in previous works [11,12]. In the following, the model is only briefly reviewed.…”

Section: Global Equivalent Circuit Modelmentioning

confidence: 99%

“…Many plasma simulation techniques focus on the plasma dynamics itself and external circuits are often neglected or drastically simplified, e.g., to a simple bias capacitance. Electrical equivalent circuit models allow to comprisingly incorporate the plasma and complex external circuits in the solution algorithms [11,12]. In contrast, Particle-in-Cell (PIC) simulations have been coupled to external series circuits consisting of a resistance, an inductance and a capacitance via conservation of charge by Verboncoeur et al [13].…”

Section: Introductionmentioning

confidence: 99%

A generic method for equipping arbitrary rf discharge simulation frameworks with external lumped element circuits

Schmidt

Trieschmann

Gergs

et al. 2019

Journal of Applied Physics

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External electric circuits attached to radio-frequency plasma discharges are essential for the power transfer into the discharge and are, therefore, a key element for plasma operation. Many plasma simulations, however, simplify or even neglect the external network. This is because a solution of the circuit's auxiliary differential equations following Kirchhoff's laws is required, which can become a tedious task especially for large circuits. This work proposes a method, which allows to include electric circuits in any desired radio-frequency plasma simulation. Conceptually, arbitrarily complex external networks may be incorporated in the form of a simple netlist. The suggested approach is based on the harmonic balance concept, which splits the whole system into the nonlinear plasma and the linear circuit contribution. A mathematical formulation of the influence of the applied voltage on the current for each specific harmonic is required and proposed.It is demonstrated that this method is applicable for both simple global plasma models as well as more complex spatially resolved Particle-in-Cell simulations.

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Multi frequency matching for voltage waveform tailoring

Cited by 37 publications

References 46 publications

Disparity between current and voltage driven capacitively coupled radio frequency discharges

Disparity between current and voltage driven capacitively coupled radio frequency discharges

Experimental demonstration of multifrequency impedance matching for tailored voltage waveform plasmas

A generic method for equipping arbitrary rf discharge simulation frameworks with external lumped element circuits

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