Capacitively driven radio frequency (rf) discharges are commonly used for plasma-assisted material processing. Because of the significant difference in the mobility of electrons and ions, a thin layer of sheath is always established at the boundary, which separates the discharge into two regions: quasi-neutral bulk plasma and positively charged sheath. Within the sheath, ions are accelerated by electric fields and therefore, bombard the electrode with significant energies. The ion energy distribution (IED) on the substrate is essentially important in the optimization of discharge operations. For plasmas sources typically operated at higher densities and lower pressures, the ion motion in the rf sheath is mainly collisionless since the ion mean free path is much larger than the sheath width. At high operating pressures and large sheath voltage drops, the sheaths are typically collisional.

A fast and simple model consisting of a series of computational steps is of great value to predict the plasma parameters and IEDs, given the control parameters of the discharge. Respective models for IEDs in collisionless and collisional capacitive rf sheaths are developed in this dissertation, based on the sheath models developed in late 1980s. Both models do not rely on any intermediate parameters from simulation or experimental results and only take a few seconds (collisionless) or minutes (collisional) to get the final IEDs. Ion-neutral charge exchange reactions are considered for collisional rf sheaths. Energy dependent ion mean free path is taken into account. Particle-in-cell (PIC) simulations are used to verify the previous sheath models and the IED models.

The PIC code OOPD1, being developed with a powerful capability as the development of the collisional IED model goes on, is introduced in this dissertation. Comparisons with XPDP1 are presented, which confirms OOPD1 as a trustable, friendly, and extensible simulation tool to observe the rf discharges.

Improved modeling of angled-dielectric insulation in high-voltage

systems is described for use in particle-in-cell (PIC) simulations.

Treatment of non-orthogonal boundaries is a significant challenge in

modeling angled-dielectric flashover, and conditions on boundaries are

developed to maintain uniform truncation error in discretized space

across the dielectric angles studied. Extensive effort was expended in

isolating particular operating regimes to illustrate fundamental

phenomenological surface effects that drive the discharges studied

herein; consequently, this document focuses on the phenomenology of

two specific dielectric angles at 6.12° for multiplicative breakdown

(the so-called single-surface multipactor) and 22.9° for a

non-multiplicative discharge that evolves into a dark current at

steady state.

Phenomenological results for simulations in vacuum through "ultra-low

pressures" on the order of a few hundred mTorr are presented. A

multipactor front forms via net emission of electrons from impact on

the dielectric surface, where emission leads to saturated field

conditions in the wake of the front, producing a well-defined

forward-peaked wave. A treatment of the gain and saturation

characteristics is presented, isolating the surface electric fields as

the driving contributor to both metrics. Physical models include

oftenneglected effects such as space-charge, dielectric-surface

charging, and particle distributions in energy and space. For the

discharges treated in this study, breakdown voltages of the typical

Paschen form are not applicable, since multiplicative conditions are

driven primarily by surface effects.

Phenomenological results are also presented for simulations at low

pressure (~ 1Torr), which is shown to be a transitional limit where

volume effects become appreciable compared to surface effects. A

coupling between space charge and surface charge is shown to lead to

oscillatory effects in otherwise DC discharges. Surface multipactor

leads to increased ionization and space charge, and the ensuing

space-charge momentum alters what would have been a steady-state

saturation as in the case of vacuum-like discharges. Models for

diffusive outgassed species are developed and implemented, extending

the capabilities of the PIC suite.

The overarching theme of this study is to communicate the dependence

of multiplicative discharges dominated by surface effects on

near-surface electric field conditions. It is shown through various

examples from vacuum through low pressures, and in diffusive gases,

that single-surface multipactor conditions can be expressed solely in

terms of the dielectric surface field angles. This treatment lays the

foundation for a novel extension of RF breakdown susceptibility theory

[1] to the DC regime, grounding breakdown susceptibility to the

well-established fundamentals on secondary emission [2, 3]. This

theory shows that breakdown characteristics can be modeled in an

a-priori framework, hence the lack of a Paschen-type curve.

Finally, the effect of the seed source on discharge characteristics is

also studied. A comparison between a constant-waveform source, a

Fowler-Nordheim source, and an application of a modified source based

on theoretical treatment from [4] are presented, showing that the seed

is a necessary but insufficient condition for surface flashover, where

the dominant contributor is the configuration of the surface fields

downstream of the seed source. While the seed can influence upstream

conditions to alter the injected current, the gain characteristics of

the downstream region are still well described by the framework

developed in the remainder of this document.