The spatiotemporal evolution of charged species densities and wall fluxes during the afterglow of an electronegative discharge has been investigated. The decay of a plasma with negative ions consists of two stages. During the first stage of the afterglow, electrons dominate plasma diffusion and negative ions are trapped inside the vessel by the static electric field; the flux of negative ions to the walls is nearly zero. During this stage, the electron escape frequency increases considerably in the presence of negative ions, and can eventually approach free electron diffusion. During the second stage of the afterglow, electrons have disappeared, and positive and negative ions diffuse to the walls with the ion-ion ambipolar diffusion coefficient. Theories for plasma decay have been developed for equal and strongly different ion (T(i)) and electron (T(e)) temperatures. In the case T(i)=T(e), the species spatial profiles are similar and an analytic solution exists. When detachment is important in the afterglow (weakly electronegative gases, e.g., oxygen) the plasma decay crucially depends on the product of negative ion detachment frequency (gamma(d)) and diffusion time (tau(d)). If gamma(d)tau(d)>2, negative ions convert to electrons during their diffusion towards the walls. The presence of detached electrons results in "self-trapping" of the negative ions, due to emerging electric fields, and the negative ion flux to the walls is extremely small. In the case T(i)<
A self-consistent 1-D model was developed to study the effects of non-local electron conductivity on power absorption and plasma density profiles in a planar inductively coupled argon discharge at low pressures (≤ 10 mTorr). The model consisted of three modules: (1) an electron energy distribution function (EEDF) module to compute the non-Maxwellian EEDF, (2) a non-local electron kinetics module to predict the non-local electron conductivity, RF current, electric field and power deposition profiles in the non-uniform plasma, and (3) a heavy species transport module to solve for the ion density and velocity profiles as well as the metastable density. Results using the non-local electron conductivity model were compared with predictions of a local theory (Ohm's law), under otherwise identical conditions. The RF current, electric field, and power deposition profiles were very different, especially at 1 mTorr for which the effective electron mean free path was larger than the skin depth. However, the plasma density profiles were almost identical (within 10%) for the same total power deposition in the plasma. This result suggests that, for computing plasma density profiles, a local conductivity model (Ohm's law), with much reduced computational expense, may be employed even in the non-local regime. INTRODUCTIONInductively coupled plasma (ICP) sources can produce a high-density, uniform plasma in a low pressure gas without the need for external magnetic fields [1,2,3,4,5]. Such sources are used extensively for etching and deposition of thin films in microelectronics manufacturing.At higher pressures (above ≈ 20 mTorr), electrons in an ICP discharge are heated by collisional dissipation of wave energy. However, both experimental and theoretical results in lower pressure discharges, indicate that power deposition involves a collisionless electron heating mechanism [6,7]. It has been suggested that in both planar [8] and solenoidal [4] ICP discharges, the collisionless heating mechanism is a "warm plasma" effect analogous to the anomalous skin effect in metals.The anomalous skin effect in gas discharges was first studied analytically by Weibel [9] for a semi-infinite plasma with uniform electron density. Further analytical work was performed for a non-uniform density, semi-infinite plasma with a "diffuse boundary" by Liberman et al. [10], and for an infinite plasma with a "diffuse boundary" by Dikman et al. [11]. Early experimental investigation of the skin effect was performed by Demirkhanov et al.[12] for a cylindrical "ring" discharge.The anomalous skin effect in 1-D (slab geometry) bounded plasmas has been studied theoretically and experimentally in [13,14] for a symmetric power source (a current sheet on either side of the slab), and in [15,16] for an asymmetric source. An interesting effect associated with bounded plasmas is the possible resonance between the wave frequency and the motion of electrons bouncing between the walls. This can lead to enhanced heating [15,17,18]. However, as shown in Ref. 19, if the elec...
A two-dimensional self-consistent continuum model was developed to study the spatio-temporal dynamics of a pulsed power (square-wave-modulated) inductively coupled electropositive (argon) discharge. The coupled equations for plasma power deposition, electron temperature and charged and neutral species densities were solved to obtain the space-time evolution of the discharge in a gaseous electronics conference (GEC)-ICP reference cell. The Ar* metastable density was governed by gas phase reactions since the diffusion time was longer than the pulse period. This resulted in complex Ar* density profiles as a function of time during a pulse. The time-average ion flux to the substrate in the pulsed plasma reactor was larger than that in a continuous wave reactor, for the same energy input. The effect of control parameters such as power, duty ratio, pressure and pulse frequency on the evolution of electron density was investigated. Simulation results on electron density and temperature were in reasonable agreement with available experimental data.
Negative ion density fronts have been shown to occur in electronegative steady-state plasmas with hot electrons. In this Letter, we report theoretical and numerical results on the spatiotemporal evolution of negative ion density fronts during plasma ignition and extinction (afterglow). During plasma ignition, the negative ion fronts are analogous to hydrodynamic shocks. This is not the case during plasma extinction where, although negative ions diffuse freely in the plasma core, the negative ion front propagates towards the chamber walls with a nearly constant velocity.
A two-dimensional (r,z) continuum model was developed to study the spatiotemporal dynamics of a pulsed power (square-wave modulated) chlorine discharge sustained in an inductively coupled plasma (ICP) reactor with a planar coil. The self-consistent model included Maxwell’s equations for the power deposition profiles coupled to the electron energy equation and the species mass balances. Simulation results showed separation of the plasma into an electronegative core and an electropositive edge during the active glow (power on) and the formation of an ion–ion plasma ∼15 μs into the afterglow (power off). During the early active glow, the negative ion flux was convection dominated near the quartz window of the ICP reactor due to the formation of large electrostatic fields, leading to a self-sharpening front propagating into the plasma. The negative ion density profiles were found to have a strong spatial dependence underlying the importance of spatial resolution in negative ion density measurements. The time dependent ion and radical flux uniformity was also studied. Simulation results were compared with experimental data and reasonable agreement was observed.
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