Electron transport to a substrate in a radio frequency capacitively coupled plasma by the Boltzmann equation

Matsui, Jun; Shibata, Mari; Nakano, Nobuhiko; Makabe, Toshiaki

doi:10.1116/1.580985

Cited by 11 publications

(4 citation statements)

References 12 publications

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“…The numerical procedure is the same as in our previous model calculation. 14,15 Fluxes to the walls of the trench were determined in each time step and the wall charge densities were estimated temporally. The resulting potentials were then calculated and the next step of simulation in the revised potential was carried out.…”

mentioning

confidence: 99%

The effect of topographical local charging on the etching of deep-submicron structures in SiO2 as a function of aspect ratio

Matsui¹,

Nakano²,

Petrović³

et al. 2001

Applied Physics Letters

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Physical and electrical influences on plasma etching on the inside of a microtrench in SiO 2 were numerically investigated using Monte Carlo simulation of ions and electrons with the aid of surface charge continuity and Poisson's equation. When the aspect ratio is greater than seven, the bottom is charged up to a potential sufficient to prevent the influence of all the incident ions, with a realistic initial energy of 300 eV for SiO 2 etching within the period required for monolayer stripping, resulting in etch stop. The cause of etch stop is purely the result of the electrical local charging due to the topography of the trench, and of the initial conditions for incident charged particles. The etch stop caused by a cw plasma will be disorganized or prevented within a short time by the aid of ion-ion plasma in an afterglow phase.

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confidence: 99%

The effect of topographical local charging on the etching of deep-submicron structures in SiO2 as a function of aspect ratio

Matsui¹,

Nakano²,

Petrović³

et al. 2001

Applied Physics Letters

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“…at 100 mTorr and 13.56 MHz having a pulsively operated opposed-substrate in 1D position space was studied by using a relaxation continuum model [103] extended to a phase space solution method of electrons [104]. This is a development of the DNP in equation (58) of electrons into the phase space.…”

Section: Effect Of Crossed Electric and Magnetic Fieldsmentioning

confidence: 99%

Velocity distribution of electrons in time-varying low-temperature plasmas: progress in theoretical procedures over the past 70 years

Makabe

2018

Plasma Sources Sci. Technol.

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A time-varying low-temperature plasma sustained by electrical powers with various kinds of fRequencies has played a key role in the historical development of new technologies, such as gas lasers, ozonizers, micro display panels, dry processing of materials, medical care, and so on, since World War II. Electrons in a time-modulated low-temperature plasma have a proper velocity spectrum, i.e. velocity distribution dependent on the microscopic quantum characteristics of the feed gas molecule and on the external field strength and the frequency. In order to solve and evaluate the time-varying velocity distribution, we have mostly two types of theoretical methods based on the classical and linear Boltzmann equations, namely, the expansion method using the orthogonal function and the procedure of non-expansional temporal evolution. Both methods have been developed discontinuously and progressively in synchronization with those technological developments. In this review, we will explore the historical development of the theoretical procedure to evaluate the electron velocity distribution in a time-varying low-temperature plasma over the past 70 years.

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“…They employed the two‐term approximation, assuming that the anisotropic part of the distribution responds fully to the time variations of the field (quasi steady‐state approximation). A direct solution of the Boltzmann equation, neglecting electron‐electron collisions, was employed by Matsui et al in their relaxation continuum‐Boltzmann equation model …”

Section: Hybrid Models and Simulationsmentioning

confidence: 99%

Hybrid Simulation of Low Temperature Plasmas: A Brief Tutorial

Economou

2016

Plasma Processes & Polymers

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Modeling and simulation of low temperature plasmas is widely accepted as a useful tool from both physics and plasma reactor design points of view. Of the modeling approaches, hybrid models strive to combine the predictability of kinetic models with the lower computational burden of fluid models. This paper presents a brief tutorial of hybrid plasma modeling and representative simulation results using hybrid models. Whenever possible, these results are compared to kinetic and/or fluid simulations as well as experimental data.

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Electron transport to a substrate in a radio frequency capacitively coupled plasma by the Boltzmann equation

Cited by 11 publications

References 12 publications

The effect of topographical local charging on the etching of deep-submicron structures in SiO2 as a function of aspect ratio

The effect of topographical local charging on the etching of deep-submicron structures in SiO2 as a function of aspect ratio

Velocity distribution of electrons in time-varying low-temperature plasmas: progress in theoretical procedures over the past 70 years

Hybrid Simulation of Low Temperature Plasmas: A Brief Tutorial

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