Nonlinear series resonance and standing waves in dual-frequency capacitive discharges

Wen, De‐Qi; Kawamura, Emi; Lieberman, M. A.; Lichtenberg, A. J.; Wang, You‐Nian

doi:10.1088/0963-0252/26/1/015007

Cited by 33 publications

(44 citation statements)

References 53 publications

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“…Moreover, the ion flux can be adjusted in this way [20]. Oberberg et al [21] also found that tuning such axially non-uniform magnetic fields in low pressure CCPs allows to control the self-excitation of the plasma series resonance (PSR) and Non-Linear Electron Resonance Heating (NERH) in space and time due to the magnetic control of the plasma symmetry [22,23]. Other recent studies reported that a homogeneous B-field can lead to an asymmetry in CCP discharges and can improve the control of the ion energy and flux at boundary surfaces [24].…”

Section: Introductionmentioning

confidence: 99%

Electron power absorption dynamics in magnetized capacitively coupled radio frequency oxygen discharges

Wang

Wen

Hartmann

et al. 2020

Plasma Sources Sci. Technol.

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The influence of a uniform magnetic field parallel to the electrodes on radio frequency capacitively coupled oxygen discharges driven at 13.56 MHz at a pressure of 100 mTorr is investigated by one-dimensional Particle-in-Cell/Monte Carlo collision (1D PIC/MCC) simulations. Increasing the magnetic field from 0 to 200 G is found to result in a drastic enhancement of the electron and the O + 2 ion density due to the enhanced confinement of electrons by the magnetic field. The time and space averaged O − ion density, however, is found to remain almost constant, since both the dissociative electron attachment (production channel of O − ) and the associative electron detachment rate due to the collisions of negative ions with oxygen metastables (main loss channel of O − ) are enhanced simultaneously. This is understood based on a detailed analysis of the spatio-temporal electron dynamics.The nearly constant O − density in conjunction with the increased electron density causes a significant reduction of the electronegativity and a pronounced change of the electron power absorption dynamics as a function of the externally applied magnetic field. While at low magnetic fields the discharge is operated in the electronegative Drift-Ambipolar (DA) mode, a transition to the electropositive α-mode is induced by increasing the magnetic field. Meanwhile, a strong electric field reversal is generated near each electrode during the local sheath collapse at high magnetic fields, which locally enhances the electron power absorption. A model of the electric field generation reveals that the reversed electric field is caused by the reduction of the electron flux to the electrodes due to their trapping by the magnetic field.The consequent changes of the plasma properties are expected to affect the applications of such discharges in etching, deposition and other semiconductor processes.

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Section: Introductionmentioning

confidence: 99%

Electron power absorption dynamics in magnetized capacitively coupled radio frequency oxygen discharges

Wang

Wen

Hartmann

et al. 2020

Plasma Sources Sci. Technol.

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“…However, the mechanisms causing these harmonic excitations were not clarified. Lieberman et al [27] and Wen et al [28] brought the coupling of the PSR and SWE into focus. They developed a transmission line model which predicted that the self-excited harmonics by PSR can lead to spatial resonances, significantly enhancing the power deposition in the central region of the reactor.…”

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confidence: 99%

“…To bring the effect of harmonics into clearer focus, we employed a nonlinear electromagnetic radial transmission line model [27,28] of a highly asymmetric cylindrical discharge. The discharge was driven at r ¼ R by a voltage source V rf ¼ V 0 cos ωt having resistance R s , through a blocking capacitor C b .…”

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confidence: 99%

“…At higher pressures, the SWE at the fundamental frequency is damped, due to more frequent electron momentum transfer collision with the background gas, giving rise to a weaker initial excitation of nonlinear harmonics. This, combined with a temporally faster decay at higher pressures [28], primarily explains the suppression of higher harmonics with increasing pressure (Fig. 4), which also yields lower plasma density [ Fig.…”

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Observation of Nonlinear Standing Waves Excited by Plasma-Series-Resonance-Enhanced Harmonics in Capacitive Discharges

et al. 2019

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We report the first experimental observation of nonlinear standing waves excited by plasma-seriesresonance-enhanced harmonics in low pressure, very high frequency, parallel plate, capacitively coupled plasmas. Spatial structures of the harmonics of the magnetic field, measured by a magnetic probe, are in very good agreement with simulations based on a nonlinear electromagnetics model. At relatively low pressure, the nonlinear sheath motion generates high-order harmonics that can be strongly enhanced near the series resonance frequencies. Satisfying certain conditions, such nonlinear harmonics induce radial standing waves, with voltage and current maxima on axis, resulting in center-high plasma density. Excitation of higher harmonics is suppressed at higher pressures.

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“…Also, both z-symmetric and z-antisymmetric waves can exist in an asymmetric system, which could be responsible for the observed hysteresis. Integrating the electric fields in the z direction (see figure 2) to obtain the voltages gives a voltage description of the wave propagation modes [54][55][56].…”

Section: Symmetric and Anti-symmetric Mode Wave Propagationmentioning

confidence: 99%

Two-dimensional particle-in-cell simulations of standing waves and wave-induced hysteresis in asymmetric capacitive discharges

Wen

Kawamura

Lieberman

et al. 2017

J. Phys. D: Appl. Phys.

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Asymmetrically excited, high frequency cylindrical capacitive discharges are widely used for materials etching and thin film deposition. Two-dimensional (2D) electrostatic particle-in-cell (PIC) simulations show the existence of standing waves and wave-induced hysteresis of the plasma density, i.e. two different steady states for the same driving rf voltage amplitude, when the voltage is increased from a low value or decreased from a high value. The phenomenon is explored over a range of pressures (10-30 mTorr) and frequencies (60-80 MHz). Examined at 73 MHz, with increasing gas pressure, the hysteresis loop gradually shrinks and vanishes. To understand the hysteresis induced by z-symmetric and z-antisymmetric radial wave propagation modes, the PIC results are compared with a nonlinear transmission line model assuming uniform bulk plasma density, to determine the symmetric and antisymmetric voltage amplitudes. The model results are in good agreement with the PIC observations, showing central-low and central-high profiles of the antisymmetric mode voltage at low density and high density, respectively. The results are then used to determine the parameters of a lumped circuit model of the two modes, from which the hysteresis is induced by the density dependence of the symmetric and anti-symmetric wave mode absorbed electron powers. For the low density state, the discharge is sustained mainly by the symmetric mode excitation. At high density, the discharge is sustained by both symmetric and anti-symmetric modes, with the latter partly showing a spatial resonance. The results are also shown to be frequency dependent, with an onset of the hysteresis at about 66 MHz.

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Nonlinear series resonance and standing waves in dual-frequency capacitive discharges

Cited by 33 publications

References 53 publications

Electron power absorption dynamics in magnetized capacitively coupled radio frequency oxygen discharges

Electron power absorption dynamics in magnetized capacitively coupled radio frequency oxygen discharges

Observation of Nonlinear Standing Waves Excited by Plasma-Series-Resonance-Enhanced Harmonics in Capacitive Discharges

Two-dimensional particle-in-cell simulations of standing waves and wave-induced hysteresis in asymmetric capacitive discharges

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