Badri N. Ramamurthi

Two-dimensional pulsed-plasma simulation of a chlorine discharge

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 ...

Effect of electron energy distribution function on power deposition and plasma density in an inductively coupled discharge at very low pressures

A self-consistent one-dimensional model was developed to study the effect of the electron energy distribution function (EEDF) on power deposition and plasma density profiles in a planar inductively coupled plasma (ICP) in the non-local regime (pressure ≤10 mTorr). The model consisted of three modules: (1) an EEDF module to compute the non-Maxwellian EEDF, (2) a non-local electron kinetics module to predict the non-local electron conductivity, radio frequency (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-Maxwellian EEDF model were compared with predictions using a Maxwellian EEDF, under otherwise identical conditions. The RF electric field, current and power deposition profiles were different, especially at 1 mTorr, for which the electron effective mean-free-path was larger than the skin depth. The plasma density predicted by the Maxwellian EEDF was up to 93% larger for the conditions examined. Thus, the non-Maxwellian EEDF must be accounted for in modelling ICPs at very low pressures.

Pulsed-power plasma reactors: two-dimensional electropositive discharge simulation in a GEC reference cell

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.

Effect of non-local electron conductivity on power absorption and plasma density profiles in low pressure inductively coupled discharges

A self-consistent one-dimensional 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, radio frequency (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 (Ohms 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 (Ohms law), with much reduced computational expense, may be employed even in the non-local regime.

Self-consistent modeling of nonlocal inductively coupled plasmas

In low-pressure radio-frequency (RF) discharges, the electron-energy distribution function (EEDF) is typically non-Maxwellian for low plasma density. The nonlocal plasma conductivity, plasma density profiles, and EEDF are all nonlinear and nonlocally coupled. For accurate calculation of the discharge characteristics, the EEDF needs to be computed self-consistently. The method of fast self-consistent one-dimensional of planar inductively coupled discharges driven by a RF electromagnetic field is presented. The effects of a non-Maxwellian EEDF, plasma nonuniformity, and finite size, as well as the influence of the external magnetic field on the plasma properties are considered and discussed

Self-trapping of negative ions due to electron detachment in the afterglow of electronegative gas plasmas

The spatiotemporal evolution of charged species densities and wall fluxes during the afterglow of an electronegative discharge has been investigated. It was found that plasma decay crucially depends on the product of negative-ion-detachment frequency (γd) and diffusion time τd. If γdτd>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. Thus, negative ions can be extracted in the afterglow only if γdτd<2.

Time evolution of an ion-ion plasma after the application of a direct current bias voltage

A one-dimensional fluid model was developed to investigate the time evolution of a positive ion-negative ion (ion-ion) plasma after the application of a direct current (dc) bias voltage. The ion mass and momentum continuity equations were coupled to the Poisson equation for the electric field. The applied bias is shielded and space charge sheaths are formed within the time scale of ion response (ion plasma frequency). When the ion collision frequency is low compared to the ion plasma frequency, electric field oscillations develop in the bulk due to the ion inertia (overshoot). The net charge density in the sheath, the sheath electric field, and the flux and energy of ions bombarding the electrodes all go through maximum values at a time comparable to the ion plasma frequency. Over long time scales the sheaths are in quasiequilibrium with the bulk plasma. At this time, the ion flux on each electrode is twice the free diffusion flux.

Effectiveness of electron-cyclotron and transmission resonance heating in inductively coupled plasmas

The electron-cyclotron and transmission resonances in magnetically enhanced low-pressure one-dimensional uniform inductively coupled plasmas are studied analytically within a simple model of two driven electrodes. The results of our approach are also applicable to the case of one grounded electrode. It is shown that, for a high discharge frequency, the plasma resistance is greatly enhanced at electron-cyclotron and transmission resonances, but normally does not exhibit a sharp peak at the electron-cyclotron resonance (ECR) condition. For a low discharge frequency, the ECR heating is not effective. Conditions of strong transmission resonances are identified. A transition from a bounded to semi-infinite plasma with overlapping of transmission resonances is also considered.

Metastable argon density evolution in a pulsed ICP discharge

A two-dimensional self-consistent plasma fluid model was developed to study the dynamics of a pulsed power inductively coupled argon discharge. The metastable Ar*(/sup 3/P/sub 0/ and /sup 3/P/sub 2/ levels) density evolution during a pulse is governed by volumetric reactions, giving rise to complex spatiotemporal behavior.

Spatio-temporal dynamics of charged species in the afterglow of plasma containing negative ions

Summary form only given. The spatio-temporal evolution of charged species densities and wall fluxes during the afterglow of an electronegative discharge have been investigated. It was found that decay of plasma with negative ions is quite different than that of electropositive plasma. Decay of plasma with negative ions consists of two surges. During first stage electrons dominate plasma diffusion and negative ions are trapped inside by the static electric field: the flux of negative ions to the walls is nearly zero. The electron escape frequency is considerably increased 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.