Energy transfer processes in glow discharges

Abril, Isabel; Gras‐Martí, A.; Vallés-Abarca, JA

doi:10.1116/1.573936

Cited by 29 publications

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“…For ex-ample, a time dependent phenomena (18,19) (10). Finally, only the average ion energy and not the ion energy distribution (8,20) can be found. Nevertheless, the simplified sheath model developed here can be readily coupled to a more general plasma etching reactor model, including transport and reaction phenomena of the etching species, to calculate etch rate, uniformity, and anistropy of etching thin films (13).…”

Section: Discussionmentioning

confidence: 99%

“…Solution of the coupled integro-differential equations subject to appropriate boundary conditions could yield the corresponding distribution functions. Such an approach is invariably difficult, although progress has recently been made in solving for the spatially dependent energy distribution functions of ions, electrons, and fast neutrals (resulting from charge exchange collisions) in a time-independent sheath (8). Another approach is to employ the Monte Carlo method as demonstrated by Kushner (9).…”

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confidence: 99%

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A Time‐Average Model of the RF Plasma Sheath

Economou

Evans

Alkire

1988

J. Electrochem. Soc.

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A time-average model of the RF plasma sheath was developed. The ion "fluid" equations were used with a frictional force to account for ion-neutral collisions. Consideration of the collision dynamics showed that the frictional force may be taken as proportional to the square of the ion drift velocity. The sheath model was used to investigate the ion energy and flux on the electrodes of plasma reactors. The dimensionless quantity Co (collision number) was found to be important in describing the ion motion in the sheath. An analytical expression for the ion bombardment energy was derived, in terms of Co and the sheath voltage, for the range of parameter values typical of high pressure (-1 torr) diode plasma etchers. An application of the model to an oxygen discharge in a parallel plate reactor was considered. Over the parameter range investigated, the ion bombardment energy was found to be only a few tens of eV, much lower than typical sheath voltages (-200V). The ion bombardment energy was found to be a function of the sheath electric-field-to-pressure ratio. The model provides a framework that can be incorporated into more general plasma reactor models which consider transport and reaction phenomena along surfaces undergoing etching.Within the last decade, dry etching using an RF diode discharge in a chemically reactive gas has become a widespread technique in the fabrication of microelectronic devices. Under conditions of relatively high pressure (-1 torr) and high frequency (-10 MHz), an RF discharge of this kind may resemble an ideal, nonequilibrium, slightly ionized plasma separated from wall and electrode surfaces by a region of positive space charge or sheath. In the sheath region ions are accelerated toward electrode or wall surfaces by the electric field present due to the space charge. In their transit through the sheath, ions may experience collisions, mainly with neutrals owing to the low degree of ionization (~<10-4). Such collisions serve to reduce the energy and randomize the ionic motion. Determination of the ion flux and the energy and angular distribution functions of ions striking the electrodes of plasma reactors is of significant technological interest in semiconductor processing. Such quantities affect both the etching rate and the degree of anisotropy in plasma etching applications. The purpose of this paper is to develop an approximate model to investigate the behavior of ionic species within the high field sheath regions of a gas discharge.Quantities that affect the energy and/or directionality of bombarding ions include the sheath electric-field-topressure ratio (E/p) (1, 2), the applied frequency (3), and the nature and topography of the surface (4, 5). The quantity E/p is a measure of the energy imparted to an ion by the electric field over the distance of one mean fl'ee path. Frequency has a pronounced effect on ion bombardment energy. At low frequencies ions can respond to the instantaneous sheath voltage and, in the absence of collisions, the maximum ion energy would correspo...

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

A Time‐Average Model of the RF Plasma Sheath

Economou

Evans

Alkire

1988

J. Electrochem. Soc.

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“…The energy and spatial distributions of (energetic) sputtered metal atoms moving through the sputtering gas have been studied in a large number of works, using both analytic [27][28][29] and numerical (mainly Monte Carlo) [6,25,30,31] approaches. The analytic approaches employ the models of continuous slowing down (CSD) of metal particles traveling along SLTs, which are a good approximation to heavy sputtered atoms in a light sputtering gas, when M m M n (where M m and M n are the masses of a sputtered metal atom and buffer-gas neutral, respectively).…”

Section: Fast Sputtered Metal Atoms and Their Thermalization Profilementioning

confidence: 99%

“…In the present work, in order to describe the fast sputtered metal atoms we shall use the SLT and CSD models of [27][28][29]. As discussed in detail in [27,28], for power-law interaction potentials describing elastic collisions between sputtered metal atoms and gas particles, the energy loss to the stopping medium per unit travelled path length ξ is given in the CSD model by dw/dξ = −α m (x) √ w, where α m = 2/A m with…”

Section: Fast Sputtered Metal Atoms and Their Thermalization Profilementioning

confidence: 99%

Model of the cathode region and gas temperature of a dc glow discharge at high current density

Arslanbekov¹

2000

J. Phys. D: Appl. Phys.

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A model is reported of the cathode region of a dc glow discharge at high current density. The distributions of most important plasma species (such as fast electrons, fast neutrals and ions, and energetic sputtered metal atoms) are determined either analytically or using simple semi-analytic methods, taking into account possible strong gas-density/temperature gradients. A heat-transfer equation is used to calculate the gas temperature, and the power-deposition profiles due to fast neutrals and energetic metal atoms are determined at the kinetic level. For the conditions of interest, the power-deposition profiles are shown to be strongly non-local and the assumption of Joule (local) heating to be generally inappropriate. Fast neutrals reflected from the cathode, as well as fast recoil neutrals, are shown to play a key role in determining the rate and spatial distribution of gas heating. Spectroscopic measurements of the gas temperature in a hollow-cathode discharge are carried out over a wide range of discharge conditions. The experimental and predicted gas temperatures are compared and acceptable agreement is found. A strong sensitivity of the model predictions to the assumed particle-surface interaction data is observed. The model can be readily adapted to other types of glow discharge and other geometries. It is computationally efficient and can be useful for fast self-consistent modelling of glow-discharge plasmas.

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“…The theoretical treatment of the transport equation, restricted to an expression for the distribution in one-dimensional velocity space, has been discussed in previous studies. [9][10][11][12][13][14] Monte Carlo simulation is performed to derive the distribution of the ions in two-dimensional velocity space. [15][16][17] A numerical approach based on the Boltzmann equation is also performed to investigate the twodimensional etching profile of dry etching.…”

Section: Introductionmentioning

confidence: 99%

Prediction of the evolution of the erosion profile in a direct current magnetron discharge

Okazawa

Shidoji

Makabe

1999

Journal of Applied Physics

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We have performed a simulation of ion and fast neutral transport in the sheath region of a direct current magnetron discharge under different pressures by using the Boltzmann equation and the database from the two-dimensional (2D) results of a plasma structure, which was given by a hybrid model. Evolution of the erosion profile on the target surface has been predicted by using the 2D energy distributions of ions and fast neutrals incident on the target (cathode) surface. We confirmed that an accurate prediction of the erosion profile can be obtained by assuming that the constant sputtering yield corresponds to the cathode voltage under conditions of low pressures that make use of the film deposition processes.

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Energy transfer processes in glow discharges

Cited by 29 publications

References 1 publication

A Time‐Average Model of the RF Plasma Sheath

A Time‐Average Model of the RF Plasma Sheath

Model of the cathode region and gas temperature of a dc glow discharge at high current density

Prediction of the evolution of the erosion profile in a direct current magnetron discharge

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