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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 90 (2001), S. 570-579 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A one-dimensional (1D) model for a methane rf plasma consisting of 20 species (neutrals, radicals, ions, and electrons) is presented. The equations solved are the particle balances, assuming a drift-diffusion approximation for the fluxes, and the electron energy balance equation. The self-consistent electric field is obtained from the simultaneous solution of Poisson's equation. The electron–neutral collision rates are expressed as a function of the average electron energy. These expressions are obtained from the solution of the Boltzmann equation using the Lorentz approximation. The results presented in this article are limited to the alpha regime, hence no secondary electrons are considered. In total, 27 electron reactions (vibrational excitation, dissociation, and ionization) have been included in the model, as well as seven ion–neutral reactions and 12 neutral–neutral reactions. The 1D fluid model yields, among others, information about the densities of the different species in the plasma. It is found that in a methane plasma C2H6, C3H8, C2H4, and C2H2 are also present at high densities, together with CH4 and H2 (inlet gases). The main radical in the plasma is CH3. At low pressure (e.g., 0.14 Torr) the most important ion is found to be CH5+, at higher pressure (e.g., 0.5 Torr) C2H5+ becomes the dominant ion. © 2001 American Institute of Physics.
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 77 (1995), S. 1868-1874 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A three-dimensional Monte Carlo model is developed to simulate the thermalization process of atoms sputtered from the cathode in a glow discharge cell. A comparison is made with a simplified analytical thermalization model and the relative importance of different interaction potentials and scattering assumptions on quantities related to thermalization is investigated. Typical results of the thermalization model are (i) the thermalization profile (which gives the distribution of the thermalized sputtered atoms), (ii) the relative amount of atoms that can reach the backplate of the discharge cell without being thermalized, and (iii) the relative amount of backscattering to the cathode. The influence of gas pressure, kind of gas, and cathode material on the thermalization process is also investigated. © 1995 American Institute of Physics.
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 79 (1996), S. 1279-1286 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The Cu atoms sputtered from the cathode and the corresponding Cu ions in an argon direct current glow discharge are described by a combination of two models: a fluid model for their overall behavior (diffusion and migration) in the entire discharge and a Monte Carlo model for the explicit transport of the Cu ions in the cathode dark space. The models are combined with other models described previously for the electrons, Ar ions, fast Ar atoms, and Ar metastables, in order to obtain an overall picture of the glow discharge. Results of the fluid model are the densities and fluxes of the Cu atoms and ions. At 100 Pa and 1000 V the Cu atom and ion densities are of the order of 1012–1013 and 1010–1011 cm−3, respectively. The ionization degree is hence about 1%, which is much higher than for Ar. The Cu ion to Ar ion density is about 6% and the Cu ion to Ar ion flux is about 5%. The energy distribution of the Cu ions bombarding the cathode is calculated with the Monte Carlo model and shows good agreement with experiment. It is characterized by a peak at maximum energy, in contrast to the energy distribution of Ar ions and fast atoms. Since sputtering increases with the bombarding energy, the amount of self-sputtering is significant, although still clearly lower than the contribution of Ar ions and fast atoms. The influence of pressure, voltage, and current on all these quantities is investigated. © 1996 American Institute of Physics.
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 78 (1995), S. 2233-2241 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A self-consistent hybrid Monte Carlo-fluid model for a direct current glow discharge is presented. The Monte Carlo part simulates the fast electrons while the fluid part describes the ions and slow electrons. Typical results of the model include collision rates of the fast electrons, energy distributions of these electrons, fluxes and densities of the different plasma species, the electric field and the potential distribution, all as a function of position from the cathode. The influence of the negative glow on the calculations in the cathode dark space is studied. Moreover the influence of three-dimensional scattering instead of forward scattering and the incorporation of side wall effects is investigated. Calculations are carried out for a range of voltages and pressures in order to study their influence on the calculated quantities. Comparison was made between total electrical currents calculated in the model and experimentally measured ones to check the validity of the model. © 1995 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 78 (1995), S. 6427-6431 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A model is developed for a direct-current glow discharge in argon by a combination of a hybrid Monte Carlo fluid model of electrons and ions in the entire discharge and a Monte Carlo model of ions and fast atoms in the cathode dark space, in which fast ion and atom impact ionization are incorporated. The relative importance of these processes, compared to electron impact ionization is investigated, as a function of distance from the cathode and at different discharge conditions. It is found that they are dominant close to the cathode, and that they gain importance with increasing voltages. With the incorporation of these processes it was possible to predict current–voltage relations which are in excellent agreement with experiment. Also, the length of the cathode dark space, as a function of pressure and voltage, is calculated; the results agree with Aston's empirical formula. © 1995 American Institute of Physics.
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 87 (2000), S. 8334-8344 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A model is developed for self-consistently calculating the gas temperature in a direct current argon glow discharge, used for analytical spectroscopy. The power input into the argon gas due to elastic (i.e., kinetic energy transfer) collisions of Ar+ ions, and fast Ar atoms, sputtered Cu atoms and electrons with the argon gas atoms is calculated with Monte Carlo models. This power input is used in a heat transfer model to calculate the gas temperature. The amount of power input, the contributions of the various input sources, and the resulting gas temperature are calculated for a wide range of voltages, pressures, and currents, typically applied in analytical spectroscopy. It is found that the temperature can increase significantly at high voltages, pressures, and currents (up to a factor of 3 compared to absolute room temperature). © 2000 American Institute of Physics.
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 86 (1999), S. 2990-3001 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A hybrid Monte Carlo-fluid model has been developed for the description of electrons, argon ions, and fast argon atoms in a capacitively coupled radio-frequency (rf) glow discharge used in analytical spectroscopy. Typical operating conditions are about 6 Torr pressure and 10 W electrical power. The discharge cell is rather small and is characterized by a much smaller rf-powered electrode than grounded electrode, which yields a high dc bias voltage. The electron density at these conditions is in the order of 1013 cm−3. The computation time to simulate all these electrons with a Monte Carlo or a particle-in-cell method was found to be too long. Therefore, the electrons are subdivided in two groups. The fast electrons emitted from the rf electrode, as well as the ones formed by ionization with sufficiently high total (=kinetic+potential) energy for further ionization, give rise to so-called γ ionization; these are described with a Monte Carlo method. The slow electrons, which can, however, be heated again by the fluctuating electric field, give rise to so-called α ionization; they are described with a fluid approach, which also treats the argon ions. Moreover, the fast argon ions and atoms are treated with a Monte Carlo model in the rf sheath. Typical results of this model include the electrical characteristics (i.e., dc bias and rf amplitude voltages, electrical current, potential, and electric field distributions), the electron densities and mean energies, the ionization rates due to the electron impact α and γ ionization and fast argon ion and atom impact ionization, and the relative contributions of these ionization mechanisms to the overall ionization. © 1999 American Institute of Physics.
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 87 (2000), S. 3628-3636 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The electron energy relaxation in space has been investigated for electropositive Ar and electronegative SiH4 discharges by a 1D Particle-in-cell/Monte Carlo code. The ionization rate has been studied since this rate is strongly influenced by the energy relaxation mechanism. The ionization rate in the two kinds of discharges at a low pressure (30 mTorr), a low power (8 W), and a low frequency (13.56 MHz) is regarded as the reference case. The effects of pressure, power, and frequency on the ionization rate have been observed and compared between the two types of discharges. With the pressure increasing from 30 to 400 mTorr, in the case of the argon discharge the ionization peak moves from the plasma bulk (nonlocal behavior of the electron energy distribution function) towards the momentary cathodic presheath (local behavior). In addition to a similar variation of the ionization rate, in the silane discharge an ionization peak occurs near the momentary anodic presheath, and at the high pressure the ionization in the plasma bulk is still considerable. The power can only influence the ionization rate quantitatively. The effect of frequency on the ionization rate is similar for both kinds of discharges. With increasing frequency the ionization rate tends to a somewhat local character, i.e., the ionization appears closer to the momentary cathode. This is attributed to the fact that at the high frequency a bulk electric field in the bulk is found clearly out of phase with the sheath fields, and the energetic electrons are pushed towards the cathode earlier in space. Meanwhile, in the silane discharge the distinctive ionization, which is strongly present at the anodic presheath and in the plasma bulk at low frequency, almost disappears. © 2000 American Institute of Physics.
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 86 (1999), S. 4124-4133 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A two-dimensional model has been developed for calculating the behavior of Ar2+ and Ar2+ ions in a direct current argon glow discharge, by the use of balance equations describing the various production and loss processes for these species, as well as their transport by diffusion and migration. These balance equations are coupled to the equations for the Ar+ ions and electrons and solved simultaneously with Poisson's equation, to obtain a self-consistent description of the charged particles behavior and the electrical characteristics in the glow discharge. Moreover, this model is combined with the other models that we have developed previously for the Ar atoms in various excited levels and the Cu atomic and ionic species, to obtain an overall description of the direct current argon glow discharge. The model is applied to typical conditions used for glow discharge mass spectrometry (pressure of 50–100 Pa, voltage of 600–1400 V, and current of 0.4–15 mA). Typical calculation results include the densities and fluxes of these ionic species, as well as the relative contributions of their production and loss processes. The Ar2+ ions are almost exclusively formed by two-electron ionization from Ar0 atoms, and they become primarily lost by diffusion and subsequent recombination at the cell walls. The Ar2+ ions are mainly created by Hornbeck–Molnar and metastable-metastable associative ionization, whereas atom to molecule conversion seems to play only a minor role at the discharge conditions under study. Loss of these Ar2+ ions is caused primarily by diffusion and recombination at the cell walls, but dissociative recombination in the plasma plays also a significant role. We found that the ratios of Ar2+/Ar+ and Ar2+/Ar+ ion densities and fluxes were in the order of 1%–10%, which is in good agreement with experimental observations. © 1999 American Institute of Physics.
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  • 10
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 84 (1998), S. 121-136 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An extensive collisional-radiative model for the argon atoms in a glow discharge has been developed. Sixty-five effective argon atomic levels are considered. The processes taken into account are radiative decay, electron, fast argon ion and argon atom and thermal argon atom impact ionization, excitation and deexcitation between all the levels, electron-ion radiative recombination, and electron-ion three-body recombination where the third body is an electron, fast argon ion or atom, or a thermal argon atom. Some additional processes are incorporated for the two 4s metastable levels, i.e., Penning ionization of sputtered atoms, two- and three-body collisions with argon ground state atoms, collisions between two atoms in a metastable level, and diffusion and subsequent deexcitation at the walls. Typical results of the model are the populations of the various excited levels as a function of distance, and the relative contributions of different populating and depopulating processes for all levels. © 1998 American Institute of Physics.
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