Modeling of the sheath and the energy distribution of ions bombarding rf-biased substrates in high density plasma reactors and comparison to experimental measurements

Edelberg, Erik A.; Aydil, Eray S.

doi:10.1063/1.371446

Cited by 130 publications

(127 citation statements)

References 24 publications

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“…In recent years, a good understanding of rf-driven sheath dynamics has emerged following extensive analytical, [3][4][5]8,9 numerical, 7,10-16 and experimental 14,31 investigations, particularly in the high-frequency regime. In the remainder of this article, we will focus our attention on the presheath response to rf bias in the low-and very low-frequency regimes.…”

Section: ͑3͒mentioning

confidence: 99%

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Effects of presheath dynamics on radio-frequency sheaths

Xiang

Waelbroeck

2003

Journal of Applied Physics

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A common approach to the study of radio frequency (rf) sheaths is to separate the description of the sheaths from that of the bulk plasma. In order to solve the resulting set of equations, an appropriate boundary condition for the sheath model has to be specified at the sheath–plasma boundary. In the existing sheath models, this boundary condition is assumed to be stationary. In present article, we investigate the ion dynamics in both presheath region and sheath region by using numerical as well as analytical methods. It is found that the presheath introduces an additional time scale ωpre=VB/l (here, ℓ is the characteristic scale of the presheath and VB is the Bohm velocity). If the rf frequency ω is low enough so that ω⩽ωpre, the boundary condition for the sheath depends on the ion dynamics in the presheath. In the very low-frequency regime ω≪VB/l, an analytical expression for the ion current is obtained which agrees well with the numerical result.

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Section: ͑3͒mentioning

confidence: 99%

“…Various sheath models have been developed using this approach. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] It is well known that ion dynamics strongly depend on the ratio of the applied rf bias frequency and the ion plasma frequency pi . In the two limits, ӷ pi and Ӷ pi , the sheath model is analytically solvable.…”

Section: Introductionmentioning

confidence: 99%

Effects of presheath dynamics on radio-frequency sheaths

Xiang

Waelbroeck

2003

Journal of Applied Physics

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“…In the model, the rf sheath field and the dust charging are determined selfconsistently by the rf sheath dynamics [21]. We also self-consistently consider all applied forces, particularly the ion drag, the neutral-gas friction, and the positiondependent excitation, acting on the microparticle and derive equations describing the motion of the particle.…”

mentioning

confidence: 99%

“…where m i , D , e, and u 0 are the ion mass, the Debye length, the elementary charge, and the ion's velocity at the sheath boundary [21], respectively. The second term in the right of Eq.…”

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confidence: 99%

“…(2) and (3) are Vz; t V 0 t and u i z; t u 0 at z 0, and Vz; t 0 at z d s t, where V 0 t is the simultaneous potential drop across the sheath and d s t is the instantaneous sheath thickness. A nonlinear equivalent circuit model [21] of the sheath can be used to determine the relation between the potential drop and the sheath thickness. Solving the above equations, we can thus obtain the average field Ez hEz; ti, the average ion density n i z hn i z; ti, and the average ion drift velocity…”

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Self-Consistent Nonlinear Resonance and Hysteresis of a Charged Microparticle in a rf Sheath

2002

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A self-consistent model is proposed to study nonlinear phenomena, such as secondary resonance and hysteresis in the vertical oscillations of a charged microparticle in a radio-frequency sheath. The motion of a single microparticle in the sheath is simulated by solving Newton's equation in which various forces acting on the particle are taken into account. The particle charging and the sheath electric field are described by a self-consistent model of the collisional radio-frequency sheath dynamics. It is found that the nonlinearity is related to the particle's charge, the sheath electric field, and the external excitation force, as well as the ion drag force and neutral-gas friction on the particle.

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Particle‐in‐cell simulation of electron and ion energy distributions in dc/rf hybrid capacitively‐coupled plasmas

2013

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A Particle‐in‐Cell simulation with Monte Carlo collisions was used to study electron and ion energy distributions (IEDs) in low‐pressure (2.67 Pa) direct‐current (dc)/radio‐frequency (rf) hybrid capacitively‐coupled Ar plasmas. One electrode (dc/rf electrode) of the parallel plate diode was powered by a 13.56 MHz source, and a negative dc bias voltage, whereas the opposite (substrate) electrode was grounded. Secondary electrons emitted from the dc/rf electrode accelerated in the adjacent sheath and entered the plasma, yielding a high‐energy tail of the electron energy distribution. For given dc bias voltage, the plasma density increased as the secondary electron emission yield due to ion bombardment increased. A fraction of the secondary electrons were energetic enough to overcome the sheath potential barrier on the substrate electrode and bombard the substrate. The electron angular distribution on the substrate electrode had a peak of directional electrons superimposed on a typical cosine distribution. The mean energy and angular spread of directional electrons could be controlled by varying the dc bias voltage. However, as the dc bias became more negative, the dc/rf sheath expanded at the expense of the bulk plasma, reducing the plasma density, in agreement with published data. The IED on the substrate electrode exhibited a dominant bimodal feature with multiple shoulder peaks due to ion‐neutral charge exchange collisions. The average ion energy decreased as the dc voltage became more negative, also in agreement with data. Pulsing the plasma power enhanced the tail of the electron energy distribution in the early activeglow (power ON), and yielded a distinct ballistic electron flux on the substrate with energy equal to the applied dc bias. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3214–3222, 2013

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Modeling of the sheath and the energy distribution of ions bombarding rf-biased substrates in high density plasma reactors and comparison to experimental measurements

Abstract: Experimental and theoretical study of ion distributions near 300 m tall steps on rf-biased wafers in high density plasmas J.

Cited by 130 publications

References 24 publications

Effects of presheath dynamics on radio-frequency sheaths

Effects of presheath dynamics on radio-frequency sheaths

Self-Consistent Nonlinear Resonance and Hysteresis of a Charged Microparticle in a rf Sheath

Particle‐in‐cell simulation of electron and ion energy distributions in dc/rf hybrid capacitively‐coupled plasmas

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