Library

Notes: The response of a radio-frequency discharge in an electronegative gas to laser-induced photodetachment is considered. The discharge is described by a numerical fluid model, including the electron energy balance. The detachment event is simulated by transforming instantaneously all or part of the negative ions into electrons in the region of the discharge passed by the laser beam. In order to avoid severe restrictions on the computational time step, the evolution of the electron density and of the electric field is solved with a fully implicit numerical method. It turns out that the relaxation towards the periodic quasisteady state is mainly governed by a simultaneous increase of the production rate of negative ions and decrease of the ionization rate. The qualitative behavior of the calculated electron decay rate is in accordance with experimental observations.

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.

Notes: A fluid model for an argon rf discharge in a cylindrical discharge chamber is presented. The model contains the particle balances for electrons and ions and the electron energy balance. A nonzero autobias voltage is obtained by imposing the condition that the time-averaged current toward the powered and grounded electrode is zero. Particle densities and ionization profiles peak strongly in front of the smaller, powered electrode. There electric fields are stronger and the electron current density is higher, resulting in more ohmic heating and therefore higher ionization rates. The radial uniformity of the plasma in front of the powered electrode gives a homogeneous ion flux toward this electrode. The asymmetric character of the profiles of the cylindrical geometry is in clear contrast with the essentially one-dimensional infinite parallel-plate geometry, which is fully symmetric with respect to the center of the discharge and has a zero dc autobias voltage. A comparison with results of a one-dimensional model shows that the average ion density, the average ion flux, and the average ionization rate in the cylindrical reactor are comparable to those in a parallel-plate reactor. The numerical treatment of the time evolution of the transport equations and Poisson's equation needs an implicit method to avoid numerical instabilities. The resulting system of discretized equations is solved by a multigrid technique. The spatial discretization uses the Sharfetter–Gummel scheme.

Notes: A numerical study on the ion and neutral angular impact energy distribution at the rf-driven electrode of a reactive ion etcher is presented. The calculations for the ions are performed using a Monte Carlo method that includes charge exchange and elastic scattering. The contribution of both collision processes to the angular ion impact energy distribution is studied. For the case that charge exchange is the only collision process, the Monte Carlo results can be checked against those of a method based on a spatially uniform and time independent collision rate. In that case, both methods yield the same ion impact energy distribution. The position, velocity, and propagation angle of the energetic neutrals created in collisions of ions with the background gas are stored. These are used as input data for a separate code that follows the evolution of the angular neutral energy distribution, taking into account (multiple) neutral elastic scattering. From the ion and neutral distributions, the number of neutrals per ion, the average impact energy, and the energy-weighted average impact angle have been derived. It is shown that these parameters are well described by simple expressions. Finally, the sputter yield is calculated. The results show that the contribution of the angular distributions of both ions and neutrals to the yield can be neglected.

Notes: The high-power density of a frequency quadrupled pulsed Nd-YAG laser has been used to photodetach electrons from negative ions in rf plasmas generated within a microwave cavity. Negative ion densities have been determined by measuring the frequency shift of the resonance transmission, the shift being caused by the photoelectrons created by irradiating the plasma with the laser pulse. By measurement of the shape of the resonance curve as a function of time and of microwave frequency, and consecutive fitting of a parabola to the top of the resonance curve, the negative ion density has been determined as a function of gas pressure, rf power, and position in the plasma. Measurements were performed in plasmas of CF4, C2F6, CHF3, and C3F8. The results indicate that the negative ion densities are about one order of magnitude larger than the electron density, which is in good agreement with a fluid model calculation. The pressure and power dependence of the electron density and of the negative ion density gives insight in the relation between the electron temperature and the macroscopic plasma parameters. Measurements as a function of the laser wavelength, using a pulsed dye laser, show that in CF4 the negative ions mainly consist of F−, whereas in C2F6 significant densities of other negative ions may occur.

Notes: Recently it was shown that, by using the analysis of electrostatic waves entering the plasma–sheath edge, the direct-current (dc) Bohm criterion also holds for discharges under radio-frequency (rf) conditions. In this paper, the influence of Bohm's criterion on the sheath characteristics for generator frequencies much higher than the ion plasma frequency has been examined by means of an analysis which is based directly on the numerical solution of the Poisson equation. The present calculations indicate that for high rf voltages the time-dependent potential profile does not always increase monotonically, even if Bohm's criterion is fulfilled. However, as this nonmonotonic behavior does not lead to a more stringent Bohm criterion, the statement that the original dc Bohm criterion also holds in the high-frequency regime is confirmed. The calculations show further that the time-dependent sheath potential is almost completely modulated in the major part of the sheath and that the modulation drops abruptly to zero close to the plasma–sheath edge.

Notes: The well-known dc Bohm criterion is extended to rf discharges. Both low- (ωrf(very-much-less-than)ωpi) and high-(ωpi (very-much-less-than) ωrf) frequency regimes are considered. For low frequencies, the dc Bohm criterion holds. This criterion states that the initial energy of the ions entering the sheath must exceed a limit in order to obtain a stable sheath. For high frequencies, a modified limit is derived, which is somewhat lower than that of the dc Bohm criterion. The resulting ion current density in a high-frequency sheath is only a few percent lower than that for the dc case.

Notes: A one-dimensional fluid model for radio-frequency glow discharges is presented which describes silane/hydrogen discharges that are used for the deposition of amorphous silicon (a-Si:H). The model is used to investigate the relation between the external settings (such as pressure, gas inlet, applied power, and frequency) and the resulting composition of the gas and the deposition rate. In the model, discharge quantities such as the electric field, densities, and fluxes of the particles are calculated self-consistently. Look-up tables of the rates of the electron impact collisions as a function of the average electron energy are obtained by solving the Boltzmann equation in a two term approximation for a sequence of values of the reduced electric field. These tables are updated as the composition of the background neutral gas evolves under the influence of chemical reactions and pumping. Pumping configuration and gas inlet are taken into account by adding source terms in the density balance equations. The effect of pumping is represented by an average residence time. The gas inlet is represented by uniformly distributed particle sources. Also the radial transport of neutrals from the discharge volume into the discharge-free volume is important. As the fluid model is one dimensional, this radial transport is taken into account by an additional source term in the density balance equations. Plasma–wall interaction of the radicals (i.e., the growth of a-Si:H) is included through the use of sticking coefficients. A sensitivity study has been used to find a minimum set of different particles and reactions needed to describe the discharge adequately and to reduce the computational effort. This study has also been used to identify the most important plasma-chemical processes and resulted in a minimum set of 24 species, 15 electron-neutral reactions, and 22 chemical reactions. In order to verify the model, including the chemistry used, the results are compared with data from experiments. The partial pressures of silane, hydrogen, disilane, and the growth rate of amorphous silicon are compared for various combinations of the operating pressure (10–50 Pa), the power (2.5–10 W), and the frequency (13.56–65 MHz). The model shows good agreement with the experimental data in the dust free α regime. Discharges in the γ′ regime, where dust has a significant influence, could not be used to validate the model. © 1997 American Institute of Physics.

Notes: The results of a two-dimensional fluid model for argon rf discharges in a closed cylindrical vacuum chamber are compared with experimental data from an amorphous silicon deposition reactor. Good agreement is obtained for the relation between the dc autobias voltage and the dissipated power in the frequency range 50–100 MHz at pressures between 12 and 90 Pa. A scaling law is presented for the relation between the power, the dc bias voltage, the rf excitation frequency, and the background pressure. The model yields a linear relation between the applied rf voltage and the dc bias voltage. This relation depends only on the geometry of the discharge chamber and shows an offset.