We present a review and analysis of ion energy distributions (IED) arriving at the target of a radio frequency (rf) discharge. We mainly discuss the collisionless regime, which is of great interest to experimentalists and modellers studying high-density discharges in which the sheath is much thinner than in conventional reactive ion etching systems.We assess what has been done so far and determine what factors influence the shape of the IEDs. We also briefly discuss collisional effects on the IEDs. Having determined the important parameters, we perform some particle-in-cell simulations of a collisionless current-driven rf sheath which show that ion modulations in an rf sheath significantly affect the IEDs when τ ion /τ rf < 1, where τ ion is the ion transit time and τ rf is the rf period.

In low-pressure capacitive radio frequency discharges, two mechanisms of electron heating are dominant: (i) Ohmic heating due to collisions of electrons with neutrals of the background gas and (ii) stochastic heating due to momentum transfer from the oscillating boundary sheath. In this work we show by means of a nonlinear global model that the self-excitation of the plasma series resonance which arises in asymmetric capacitive discharges due to nonlinear interaction of plasma bulk and sheath significantly affects both Ohmic heating and stochastic heating. We observe that the series resonance effect increases the dissipation by factors of 2-5. We conclude that the nonlinear plasma dynamics should be taken into account in order to describe quantitatively correct electron heating in asymmetric capacitive radio frequency discharges.

Two electron heating mechanisms in capacitive discharges are ohmic heating due to electron-neutral collisions and stochastic heating at the plasma edge due to momentum transfer from high voltage moving sheaths. In this work, the stochastic heating and its dependence on various parameters are determined, focusing on dual frequency discharges in which the sheath motion is driven by a combination of high and low frequency sources. Particle-in-cell (PIC) simulations are used in order to investigate the electron heating. For a uniform fixed-ion discharge in which the ions are held fixed in a uniform density profile, there is no stochastic heating, as expected. For a two-step fixed-ion discharge in which the ions are held fixed in a two-step density profile with bulk density nb and sheath density nsh&lt;nb, the stochastic heating is nearly proportional to (1−nsh∕nb)2. For a self-consistent discharge with mobile ions, the stochastic heating is well described by a “hard wall model” provided that the bulk oscillation is taken into account. These results are used to develop a stochastic heating theory for dual frequency discharges, which is compared to PIC simulations, giving good agreement.

The oopd1 particle-in-cell Monte Carlo collision (PIC-MCC) code is used to simulate a capacitively coupled discharge in oxygen. oopd1 is a one-dimensional object-oriented PIC-MC code in which the model system has one spatial dimension and three velocity components. It contains a model for planar geometry and will contain models for cylindrical and spherical geometries, and replaces the xpdx1 series, which is not object-oriented. The oopd1 also allows for different weights of simulation particles and relativistic treatment of electrons. The revised oxygen model includes, in addition to electrons, the oxygen molecule in the ground state, the oxygen atom in the ground state, the negative ion O − and the positive ions O + and O + 2. The cross sections for the collisions among the oxygen species have been significantly revised from earlier work using the xpdp1 code and the electron kinematics have been enhanced. Here we make a benchmark study and compare the oopd1 code to the well-established planar xpdp1 code and discuss the differences using a limited cross section set with O + 2 ions, O − ions and electrons as the charged particles. We compare the electron energy distribution function, the electron temperature profile, the density profiles of charged particles and electron heating rates for a capacitively coupled oxygen discharge at 50 mTorr with electrode separation of 4.5 cm. Then we explore the effect of adding O atoms and O + ions on the overall discharge.

The flow of electron and ion conduction currents across a nonlinear capacitive sheath to the electrode surface self-consistently sets the dc bias voltage across the sheath. We incorporate these currents into a model of a homogeneous capacitive sheath in order to determine the enhancement of the Ohmic and stochastic heating due to self-excitation of the nonlinear series resonance in an asymmetric capacitive discharge. At lower pressures, the series resonance can enhance both the Ohmic and stochastic heating by factors of 2–4, with the Ohmic heating tending to zero as the pressure decreases. The model was checked, for a particular set of parameters, by a particle-in-cell (PIC) simulation using the homogeneous sheath approximation, giving good agreement. With a self-consistent Child-law sheath, the PIC simulation showed increased heating, as expected, whether the series resonance is important or not.