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Register a new userSimulations of electromagnetic effects in high frequency capacitively coupled discharges using the Darwin approximation
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The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models which are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomena persist in a more realistic setting. The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented as a straightforward modification of electrostatic algorithms. The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description of technical plasmas exhibiting certain electromagnetic activity.
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An 18-level argon collisional radiative model (CRM) suitable for low pressure was established. The model can be solved by combining the optical emission spectroscopy (OES) with Langmuir probe calibration. In the capacitively coupled plasmas (CCPs) with different frequency and power, the electron temperature and density obtained by the model were compared with those measured by Langmuir probe. It is found that the calibration point at any frequency or power is suitable for the fixed pressure. This method was then applied to the diagnosis of triple-frequency (TF) CCPs, it is shown that the high frequency (HF) power mainly controls the electron density, the low frequency (LF) power mainly controls the electron temperature, and the intermediate frequency (IF) power was between the two. Compared with the dual-frequency (DF) CCPs, it is found that with the increase of IF power, the HF power can control the electron density more independently with less influence on the electron temperature.
In this work, we present the results of simulations carried out for N2-H2 capacitively coupled radio-frequency discharges, running at low pressure (0.3-0.9 mbar), low power (5-20 W), and for amounts of H2 up to 5 pct. Simulations are performed using a hybrid code that couples a two-dimensional time-dependent fluid module, describing the dynamics of the charged particles in the discharge, to a zero-dimensional kinetic module, that solves the Boltzmann equation and describes the production and destruction of neutral species. The model accounts for the production of several vibrationally and electronic excited states, and contains a detailed surface chemistry that includes recombination processes and the production of NHx molecules. The results obtained highlight the relevance of the interactions between plasma and surface, given the role of the secondary electron emission in the electrical parameters of the discharge and the critical importance of the surface production of ammonia to the neutral and ionic chemistry of the discharge.
In most PIC/MCC simulations of radio frequency capacitively coupled plasmas (CCPs) several simplifications are made: (i) fast neutrals are not traced, (ii) heavy particle induced excitation and ionization are neglected, (iii) secondary electron emission from boundary surfaces due to neutral particle impact is not taken into account, and (iv) the secondary electron emission coefficient is assumed to be constant, i.e. independent of the incident particle energy and the surface conditions. Here we question the validity of these simplifications under conditions typical for plasma processing applications. We study the effects of including fast neutrals and using realistic energy-dependent secondary electron emission coefficients for ions and fast neutrals in simulations of CCPs operated in argon at 13.56 MHz and at neutral gas pressures between 3 Pa and 100 Pa. We find a strong increase of the plasma density and the ion flux to the electrodes under most conditions, if these processes are included realistically in the simulation. The sheath widths are found to be significantly smaller and the simulation is found to diverge at high pressures for high voltage amplitudes in qualitative agreement with experimental findings. By switching individual processes on and off in the simulation we identify their individual effects on the ionization dynamics and plasma parameters. We conclude that fast neutrals and energy-dependent secondary electron emission coefficients must be included in simulations of CCPs in order to yield realistic results.
The kinetic origin of resonance phenomena in capacitively coupled radio frequency plasmas is discovered based on particle-based numerical simulations. The analysis of the spatio-temporal distributions of plasma parameters such as the densities of hot and cold electrons, as well as the conduction and displacement currents reveals the mechanism of the formation of multiple electron beams during sheath expansion. The interplay between highly energetic beam electrons and low energetic bulk electrons is identified as the physical origin of the excitation of harmonics in the current.
The mixing of N2 with H2 leads to very different plasmas from pure N2 and H2 plasma discharges. Numerous issues are therefore raised involving the processes leading to ammonia (NH3) formation. The aim of this work is to better characterize capacitively-coupled radiofrequency plasma discharges in N2 with few percents of H2 (up to 5 pct), at low pressure (0.3 to 1 mbar) and low coupled power (3 to 13 W). Both experimental measurements and numerical simulations are performed. For clarity, we separated the results in two complementary parts. The actual one (first part), presents the details on the experimental measurements, while the second focuses on the simulation, a hybrid model combining a 2D fluid module and a 0D kinetic module. Electron density is measured by a resonant cavity method. It varies from 0.4 to 5e9 cm-3, corresponding to ionization degrees from 2e-8 to 4e-7. Ammonia density is quantified by combining IR absorption and mass spectrometry. It increases linearly with the amount of H2 (up to 3e13 cm-3 at 5 pct H2). On the contrary, it is constant with pressure, which suggests the dominance of surface processes on the formation of ammonia. Positive ions are measured by mass spectrometry. Nitrogen-bearing ions are hydrogenated by the injection of H2, N2H+ being the major ion as soon as the amount of H2 is larger than 1 pct. The increase of pressure leads to an increase of secondary ions formed by ion (or radical) - neutral collisions (ex: N2H+, NH4+, H3+), while an increase of the coupled power favours ions formed by direct ionization (ex: N2+, NH3+, H2+).
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