Two-dimensional Self-consistent Fluid Model Research Articles

Fluid simulation of species concentrations in capacitively coupled N2/Ar plasmas: Effect of gas proportion

A two-dimensional self-consistent fluid model and the experimental diagnostic are employed to investigate the dependencies of species concentrations on the gas proportion in the capacitive N2/Ar discharges operated at 60 MHz, 50 Pa, and 140 W. The results indicate that the N2/Ar proportion has a considerable impact on the species densities. As the N2 fraction increases, the electron density, as well as the Ar+ and Arm densities, decreases remarkably. On the contrary, the N2+ density is demonstrated to increase monotonically with the N2 fraction. Moreover, the N density is observed to increase significantly with the N2 fraction at the N2 fractions below 40%, beyond which it decreases slightly. The electrons are primarily generated via the electron impact ionization of the feed gases. The electron impact ionization of Ar essentially determines the Ar+ density. For the N2+ production, the charge transition process between the Ar+ ions and the feed gas N2 dominates at low N2 fraction, while the electron impact ionization of N2 plays the more important role at high N2 fraction. At any gas mixtures, more than 60% Arm atoms are generated through the radiative decay process from Ar(4p). The dissociation of the feed gas N2 by the excited Ar atoms and by the electrons is responsible for the N formation at low N2 fraction and high N2 fraction, respectively. To validate the simulation results, the floating double probe and the optical emission spectroscopy are employed to measure the total positive ion density and the emission intensity originating from Ar(4p) transitions, respectively. The results from the simulation show a qualitative agreement with that from the experiment, which indicates the reliable model.

Two-dimensional simulation of argon dielectric barrier discharge excited by a Gaussian voltage at atmospheric pressure

A two-dimensional self-consistent fluid model was employed to investigate the spatiotemporal characteristics of discharges in atmospheric pressure argon (Ar) dielectric barrier discharge driven by a Gaussian voltage. The simulation results show that a discharge with multiple current pulses occurs each half-cycle in the gas gap. A transition from the Townsend mode to the glow mode is observed with the increasing applied voltage each half-cycle at a lower driving frequency (7.5 kHz). It is also found that the glow mode survives all the discharge phases at a higher driving frequency (12.5 kHz and 40 kHz). The change in the discharge mode with the driving frequency mainly lies in the fact that a lot of charged particles created in the discharge gap have no enough time to drift and diffuse around, and then these particles are assembled in the discharge space at higher frequency. Additionally, the spatial distributions of the electron density indicate that a center-advantage discharge is ignited at the driving frequencies of interest, resulting in the radial non-uniformity of discharge because of the edge effects. However, this overall non-uniformity is weakened with the driving frequency increased to 40 kHz, at which concentric ring patterns are observed. These distinct behaviors are mainly attributed to the fact that many charged particles generated are trapped in the gas gap and then accumulated to make the extension along the radial direction due to the charged particles transport and diffusion, and that the effective overlapping of a large number of avalanches induced by the increased “seed” electron density with the driving frequency. Meanwhile, the surface charged particles accumulated on the dielectric barriers are also shown to play a role in the formation of the discharge structure.

Fluid simulation of the pulsed bias effect on inductively coupled nitrogen discharges for low-voltage plasma immersion ion implantation**Project supported by the National Natural Science Foundation of China (Grant Nos. 11175034, 11335004, and 11405019) and the Important National Science and Technology Specific Project of China (Grant No. 2011 ZX 02403-001.

Planar radio frequency inductively coupled plasmas (ICP) are employed for low-voltage ion implantation processes, with capacitive pulse biasing of the substrate for modulation of the ion energy. In this work, a two-dimensional (2D) self-consistent fluid model has been employed to investigate the influence of the pulsed bias power on the nitrogen plasmas for various bias voltages and pulse frequencies. The results indicate that the plasma density as well as the inductive power density increase significantly when the bias voltage varies from 0 V to 4000 V, due to the heating of the capacitive field caused by the bias power. The fraction increases rapidly to a maximum at the beginning of the power-on time, and then it decreases and reaches the steady state at the end of the glow period. Moreover, it increases with the bias voltage during the power-on time, whereas the fraction exhibits a reverse behavior. When the pulse frequency increases to 25 kHz and 40 kHz, the plasma steady state cannot be obtained, and a rapid decrease of the ion density at the substrate surface at the beginning of the glow period is observed.

Influence of dielectric materials on uniformity of large-area capacitively coupled plasmas for N2/Ar discharges**Project supported by the National Natural Science Foundation of China (Grant Nos. 11335004 and 11405019) and the Important National Science and Technology Specific Project of China (Grant No. 2011ZX02403-001).

The effect of the dielectric ring on the plasma radial uniformity is numerically investigated in the practical 450-mm capacitively coupled plasma reactor by a two-dimensional self-consistent fluid model. The simulations were performed for N2/Ar discharges at the pressure of 300 Pa, and the frequency of 13.56 MHz. In the practical plasma treatment process, the wafer is always surrounded by a dielectric ring, which is less studied. In this paper, the plasma characteristics are systematically investigated by changing the properties of the dielectric ring, i.e., the relative permittivity, the thickness and the length. The results indicate that the plasma parameters strongly depend on the properties of the dielectric ring. As the ratio of the thickness to the relative permittivity of the dielectric ring increases, the electric field at the wafer edge becomes weaker due to the stronger surface charging effect. This gives rise to the lower ion density, flux and N atom density at the wafer edge. Thus the homogeneous plasma density is obtained by selecting optimal dielectric ring relative permittivity and thickness. In addition, we also find that the length of the dielectric ring should be as short as possible to avoid the discontinuity of the dielectric materials, and thus obtain the large area uniform plasma.

Prediction of nested complementary pattern in argon dielectric-barrier discharge at atmospheric pressure.

A two-dimensional self-consistent fluid model was employed to investigate the spatiotemporal nonlinear behavior in an argon glow-like/Townsend-like dielectric-barrier discharge (DBD) at atmospheric pressure. The discharge is characterized by a major current pulse with a residual one ahead per half cycle of the external voltage. The two current pulses are operated in glow mode, but with Townsend mode between them. Contrasting spatial discharge structures are complementarily presented not only at two current pulses in the same half cycle but also during the discharge in the two adjacent-half cycles, resulting in the formation of a unique nested complementary pattern each cycle. This peculiar behavior mainly lies in the fact that sufficient charged particles are trapped in the gas gap due to the last discharge and able to dominate the subsequent discharge through the “spatial memory effect”. The charge transport regime reveals that this nested complementary pattern is presented only in a limited range of driving frequency.

Discontinuity of mode transition and hysteresis in hydrogen inductively coupled plasma via a fluid model**Project supported by the National Natural Science Foundation of China (Grant Nos. 11175034, 11205025, 11305023, and 11075029).

A new type of two-dimensional self-consistent fluid model that couples an equivalent circuit module is used to investigate the mode transition characteristics and hysteresis in hydrogen inductively coupled plasmas at different pressures, by varying the series capacitance of the matching box. The variations of the electron density, temperature, and the circuit electrical properties are presented. As cycling the matching capacitance, at high pressure both the discontinuity and hysteresis appear for the plasma parameters and the transferred impedances of both the inductive and capacitive discharge components, while at low pressure only the discontinuity is seen. The simulations predict that the sheath plays a determinative role on the presence of discontinuity and hysteresis at high pressure, by influencing the inductive coupling efficiency of applied power. Moreover, the values of the plasma transferred impedances at different pressures are compared, and the larger plasma inductance at low pressure due to less collision frequency, as analyzed, is the reason why the hysteresis is not seen at low pressure, even with a wider sheath. Besides, the behaviors of the coil voltage and current parameters during the mode transitions are investigated. They both increase (decrease) at the E to H (H to E) mode transition, indicating an improved (worsened) inductive power coupling efficiency.

Modulations of the plasma uniformity by low frequency sources in a large-area dual frequency inductively coupled plasma based on fluid simulations

As the wafer size increases, dual frequency (DF) inductively coupled plasma (ICP) sources have been proposed as an effective method to achieve large-area uniform plasma processing. A two-dimensional (2D) self-consistent fluid model, combined with an electromagnetic module, has been employed to investigate the influence of the low frequency (LF) source on the plasma radial uniformity in an argon DF discharge. When the DF antenna current is fixed at 10 A, the bulk plasma density decreases significantly with the LF due to the less efficient heating, and the best radial uniformity is obtained at 3.39 MHz. As the LF decreases to 2.26 MHz, the plasma density is characterized by an edge-high profile, and meanwhile the maximum of the electron temperature appears below the outer two-turn coil. Moreover, the axial ion flux at 3.39 MHz is rather uniform in the center region except at the radial edge of the substrate, where a higher ion flux is observed. When the inner five-turn coil frequency is fixed at 2.26 MHz, the plasma density profiles shift from edge-high over uniform to center-high as the LF coil current increases from 6 A to 18 A, and the best plasma uniformity is obtained at 14 A. In addition, the maximum of the electron temperature becomes lower with a second peak appears at the radial position of r = 9 cm at 18 A.

Equivalent circuit effects on mode transitions in H2 inductively coupled plasmas

It is well known experimentally that the circuit matching network plays an important role in the mode transition behavior of inductively coupled plasmas. To date, however, there have been no reports of numerical models being used to study the role of the matching circuit in the transition process. In this paper, a new two-dimensional self-consistent fluid model that couples the components of an equivalent circuit module is developed to investigate the effects of the equivalent circuit on the mode transition characteristics of an inductively coupled, hydrogen plasma. The equivalent circuit consists of a current source, impedance matching network, reactor impedance, and plasma transferred impedance. The nonlinear coupling of the external circuit with the internal plasma is investigated by adjusting the matching capacitance at a fixed input current. The electron density and temperature as well as the electromagnetic fields all change suddenly, and the E to H mode transition occurs abruptly at a certain matching capacitance as the impedance matching of the external circuit is varied. We also analyze the fields and the plasma characteristics during the transition process, especially for the case of the capacitive E mode.

Fluid simulation and experimental validation of plasma radial uniformity in 60 MHz capacitively coupled nitrogen discharges

A two-dimensional self-consistent electrostatic fluid model and the experimental diagnostic method are employed to investigate the plasma radial uniformity in capacitively coupled nitrogen discharges driven at 60 MHz. The effects of the rf power and electrode gap on the spatial profiles of the N2+ ion density and the radial profiles of the ion flux to the lower electrode are demonstrated. It is found in the simulation that with the increase of rf power or the decrease of electrode gap, the electrostatic edge effect becomes remarkable, which gives rise to an increase in the positive ion density at the electrode edge and thus the radial uniformity of plasma becomes worse. Moreover, the radial profiles of the N2+ ion flux to the lower electrode show a similar behavior to that of the ion density. These results are further understood by the calculated axial and radial components of the power deposition, which exhibit pronounced peaks at the electrode edge at high rf power or small electrode gap. In order to validate the simulation results, the radial profiles of the N2+ ion density were measured by a floating double probe. A general qualitative agreement between the experimental and calculated results is achieved.

Mechanisms of Streamer Propagation Affected by Driven Voltage Polarity in a Cold Atmospheric Pressure Plasma Jet

A two-dimensional self-consistent fluid model is used to investigate the effects of DC-voltage polarity in plasma initiation and propagation of helium plasma jet. The simulation results indicate that the difference in initial breakdown for the positive jet and negative jet leads to a difference in the electron density of about 4 orders of magnitude, even with the same initial electric field, which also influences the subsequent propagation. In the propagation process of negative jets, the ionization process exists in a longer gas channel behind the streamer head. In addition, the drift process to the infinite grounded electrode driven by the electric field results in higher energy consumption in the ionization process. However, in the positive jet, the ionization process mainly exists in the streamer head. Therefore, the differences in the initial breakdown and propagation process make the electric field intensity and the ionization weaker in the streamer head of the negative jet, which explains the weaker and shorter appearance of the negative jet compared to the positive jet. Our model can adequately reproduce the experimental results, viz. a bullet-like propagation in the positive jet and a continuous plasma plume in the negative jet. Furthermore, it also indicates that the streamer velocity shows the same variations as the electron drift velocity for both positive and negative jets.

Spatial Uniformity of Atmospheric Pressure Discharges: A Simulation Study

AbstractSpatial uniformity is important in most applications of dielectric barrier discharges operating at atmospheric pressure. However, such uniformity is not easily achieved. Under many conditions, a filamentary structure usually develops. In this paper, we employ a two‐dimensional self‐consistent fluid model to explore the influence of several factors on the evolution of spatial structure of dielectric barrier discharges. In particular, we contrast the behavior of discharges in pure helium and He‐N2 gas mixture, which represent the reduction in breakdown voltage of gas during the evolvement of uniform glow discharge plasma. The transformation from filamentary to uniform mode of discharge plasma is analyzed by the phenomenon of coalescence of filaments and we investigate the effect of several external discharge parameters, such as driving frequency and effect of overvoltage, and the dielectric constant of the barrier material for the uniform and filamentary discharge plasmas. This simulation study is useful to describe the spatio‐temporal profiles of electron density in different phases of the filamentary, uniform Townsend and glow discharge regimes under various constraints. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effects of reactor geometry and frequency coupling on dual-frequency capacitively coupled plasmas

In dual-frequency (DF) capacitively coupled plasma discharges, the effect of reactor geometry on the plasma density is investigated by means of a two-dimensional self-consistent fluid model combined with a power supply computation module. The results indicate that by enlarging the inter-electrode gap or by blocking the electrode with dielectric materials, the plasma density becomes more uniform along the radial direction due to the suppressed edge effect. Different approaches of the connections of the DF sources show that the distribution of plasma density is mostly confined within the blocked high-frequency (HF)-driven electrode region. Considering the asymmetry electrode shape effect, a higher plasma density could be obtained by connecting the HF source on a smaller electrode. When considering the two methods of source coupling, the DF sources applied individually on opposite electrodes may produce a higher density in comparison with the sources applied on the same electrode.

Fluid simulation of the phase-shift effect in Ar/CF4 capacitively coupled plasmas

A two-dimensional self-consistent fluid model combined with the full set of Maxwell equations is employed to investigate an Ar/CF4 capacitively coupled plasma, focusing on the phase-shift effect on the plasma characteristics at various frequencies and gas mixture ratios. When the discharge is sustained by a single frequency at 13.56 MHz in an Ar/CF4 mixture with a ratio of 0.9/0.1, no obvious difference is detected between the electron densities obtained in the so-called electrostatic model (with only the static electric fields taken into account) and the electromagnetic model (which includes the electromagnetic effects). However, as the frequency increases to 60 and 100 MHz, the difference becomes distinct, due to the significant influence of the electromagnetic effects.The phase-shift effect on the plasma radial uniformity has also been investigated in a dual frequency discharge, i.e. when the top driven source is switched on with a phase difference φ ranging from 0 to π, in the frequency range 13.56–100 MHz. At low concentration of CF4 (10%), Ar+ ions are the major positive ions in the entire range of frequencies. When the frequency is low, i.e. 13.56 MHz, the Ar+ density exhibits an off-axis peak at φ = 0 due to the edge effect, and a better uniformity caused by the phase-shift modulation is obtained at φ = π. At 60 MHz, the Ar+ density varies from edge-peaked at φ = 0 to uniform (i.e. at φ = 0.53π), and finally at φ = π, a broad maximum is observed at the centre due to the standing-wave effect. As the frequency increases to 100 MHz, the best radial uniformity is reached at 0.25π, and the maximum moves again towards the radial wall in the reverse-phase case (φ = π) due to the dominant skin effect.When the frequency is fixed at 100 MHz, the phase-shift control shows a different behaviour at a high concentration of CF4. For instance, the density profiles shift from edge-high over uniform to centre-high, as the CF4 content increases from 10% to 90%, which indicates that the skin effect is suppressed by the high electronegativity of the Ar/CF4 = 0.1/0.9 mixture. Moreover, the ratio of the total negative ion density to electron density decreases with increasing frequency, and it increases with CF4 content. In addition, ions become the major positive ions in the discharge with 90% CF4.

Fluid simulation of the phase-shift effect in hydrogen capacitively coupled plasmas: I. Transient behaviour of electrodynamics and power deposition

A two-dimensional self-consistent fluid model coupled with the full set of Maxwell equations is established to investigate the phase-shift effect on the transient behaviour of electrodynamics and power deposition in a hydrogen capacitively coupled plasma. The effect has been examined at 13.56 MHz and 100 MHz, respectively, because of the different phase-shift modulation when the electromagnetic effects are dominant. The results indicate that the spatiotemporal distributions of the plasma characteristics obtained for various phase-shift cases are obviously different both in shape and especially in absolute values. Indeed, when the phase difference varies from 0 to π, there is an increase in the electron flux, thus the power deposition becomes more pronounced. At the frequency of 13.56 MHz, the axial electron flux in the bulk plasma becomes uniform along the z-axis, and the radial electron flux exhibits two peaks within one period at the reverse-phase case, whereas the oscillation is less pronounced at the in-phase case. Furthermore, in the very high frequency discharge, the radial electron flux is alternately positive and negative with four peaks during one period, and the ionization mainly occurs in the sheath region, due to the prominent power deposition there at a phase difference equal to π.

Phase-shift effects on growth and transport of dust particles in VHF capacitively coupled silane discharges: Two dimensional fluid simulation

A two-dimensional (2D) self-consistent fluid model is developed to describe the formation, subsequent growth, transport, and charging mechanisms of nanoparticles in a capacitively coupled silane discharge applied by two very high frequency (VHF) sources with phase shift. In this discharge process, large anions are produced by a series of chemical reactions of anions with silane molecules, while the lower limit of the initial nanoparticles are taken as large anions (Si12H25- and Si12H24-) to directly link the coagulation module with the nucleation module. And then, by using the coagulation module, the particle number density quickly decreases over several orders of magnitude, whereas the particle size strongly increases. We investigate in particular the growth of the nanoparticles ranging in size from ∼1 to 50 nm in coagulation processes. The influences of controlled phase shifts between VHF (50 MHz) voltages on the electron density, electron temperature, nanoparticle uniformity, and deposition rate, are carefully studied. It is found from our simulation that the plasma density and nanoparticle density become center high and more uniform as the phase shift increases from 0 to 180°. Moreover, the role of phase-shift control in the silane discharge diluted with hydrogen gas is also discussed.

Numerical study on rectangular microhollow cathode discharge

Rectangular microhollow cathode discharge in argon is investigated by using two-dimensional time-dependent self-consistent fluid model. The electric potential, electric field, particle density, and mean electron energy are calculated. The results show that hollow cathode effect can be onset in the present configuration, with strong electric field and high mean electron energy in the cathode fall while high density and quasineutral plasma in the negative glow. The potential well and electric filed reversal are formed in the negative glow region. It is suggested that the presence of large electron diffusion flux necessitates the field reversal and potential well.

Comparison of electrostatic and electromagnetic simulations for very high frequency plasmas

A two-dimensional self-consistent fluid model combined with the full set of Maxwell equations is developed to investigate an argon capacitively coupled plasma, focusing on the electromagnetic effects on the discharge characteristics at various discharge conditions. The results indicate that there exist distinct differences in plasma characteristics calculated with the so-called electrostatic model (i.e., without taking into account the electromagnetic effects) and the electromagnetic model (which includes the electromagnetic effects), especially at very high frequencies. Indeed, when the excitation source is in the high frequency regime and the electromagnetic effects are taken into account, the plasma density increases significantly and meanwhile the ionization rate evolves to a very different distribution when the electromagnetic effects are dominant. Furthermore, the dependence of the plasma characteristics on the voltage and pressure is also investigated, at constant frequency. It is observed that when the voltage is low, the difference between these two models becomes more obvious than at higher voltages. As the pressure increases, the plasma density profiles obtained from the electromagnetic model smoothly shift from edge-peaked over uniform to a broad maximum in the center. In addition, the edge effect becomes less pronounced with increasing frequency and pressure, and the skin effect rather than the standing-wave effect becomes dominant when the voltage is high.

Modeling and experiments of high-pressure VHF SiH 4/H 2 discharges for higher microcrystalline silicon deposition rate

The effect of the total gas pressure (1–3 Torr) on the growth rate and the crystalline volume fraction (Xc) of films deposited from 70 MHz SiH 4/H 2 plasmas is investigated. The films were grown in conditions near the transition from microcrystalline to amorphous silicon growth at high deposition rates (10 Å/s). Simultaneously, a two-dimensional self-consistent fluid model of diluted SiH 4 in H 2 discharges was used to simulate the deposition process. The model integrates a detailed gas phase and surface chemistry including 25 species, 85 gas phase reactions and 27 surface reactions. A good agreement was found between model and experiments concerning the deposition rate. On this basis, the effects of pressure on the electron density and temperature, discharge impedance, electric field distribution as well as on the distribution and importance of the films precursors is discussed.

Two-dimensional simulation of the effects of the driving waveforms on the shadow mask PDP cell discharge

A new type of ac plasma display panel (PDP) with shadow mask (SM-PDP) is presented for its effective structures with lower cost. A two-dimensional self-consistent fluid model is used to analyse the discharge characteristics of the SM-PDP cell in a simplified driving scheme. The effects of the addressing time, the sustaining frequency, the duty ratio of the sustain voltage and the rise time of the voltage pulse on the discharge efficiency are investigated in this paper. The simulation results can help us optimize the driving scheme of SM-PDP.

Simulation of self-erase discharge waveforms in plasma display panels

We use a two-dimensional self-consistent fluid model to simulate the operation of a plasma display panel cell when different sustaining voltage waveforms are applied to its electrodes. The discharge path is much longer when a self-erase discharge waveform is used instead of the standard waveform. The longer discharge path results in higher efficiency.