Session TF2: Plasma Modeling and Simulation

Finite Penetration Depth Model for 2D and 3D Simulation of Etching, Deposition, and Implantation

Chemical and physical processes of plasma-solid interactions in materials processing are very diverse and complex. Final results often involve a few competing mechanisms such, for example, as etching and deposition, which go on simultaneously. The general feature profile simulator, FPS-3D [1], was developed with the goal of simulating process results for different conditions, chemistry, and materials. While low-energy species interact only with the surface mono-layer of solid materials, ions or fast neutrals could penetrate deeply inside materials. In a case of polymer deposition layers, energetic species might go through them and lead to etching of main materials. To take those effects into account, FPS-3D computes penetration depth of any energetic particle. Of course, calculating penetration depth is a complex and time consuming task by itself, especially for chemically complex targets. We are using the Range code results for that, and FPS-3D quickly computes penetration depth by spline interpolation of Range data. To demonstrate how etching, deposition, and implantation are treated by FPS-3D, we consider the case of SiO2 etching in fluorocarbon-argon-oxygen plasma in a capacitive-type plasma system. \\[4pt] [1] P. Moroz, APS-DPP, NP8, Atlanta, GA, 2009.   

Particle-in-cell/Monte Carlo simulation of capacitively coupled chlorine plasmas

A better understanding of capacitively coupled plasmas (CCP) is still important, because of the development of dual-frequency CCP discharges, and also of the CCP mode that occurs in inductively coupled plasma discharges at low rf powers. This paper presents a two-dimensional particle-in-cell/Monte Carlo (PIC/MC) simulation of CCP chlorine discharges in an asymmetric parallel-plate rf plasma reactor. The model includes an external electrical circuit with a blocking capacitor and an rf power supply, which gives self-consistently the dc self-bias voltages on the powered electrode. Four charged species (e-, Cl$_{2}$+, Cl+, Cl-) are taken into account in uniformly distributed Cl$_{2}$ neutral backgrounds, together with electron-neutral elastic collision and ionization, dissociative attachment, positive ion-neutral elastic collision and charge transfer, and electron-ion and ion-ion recombination. The results indicated that the population of negative ions dominates that of electrons, which governs the plasma discharge and sheath dynamics, and thus the dynamics of incoming ion fluxes onto the powered electrode.   

Global Model of Atmospheric Pressure Plasmas with Capacitively-Coupled Radio-Frequency Excitation

Radio-frequency driven atmospheric pressure plasma jets (rf-APPJs) provide a rich non-thermal afterglow chemistry, which offers new opportunities for the treatment of delicate materials, e.g. in biomedicine. A global model for the electron temperature and the electron density in the plasma bulk of such discharges is developed. The concept is based on the balance between the ohmic heating power, absorbed by the electrons, and the corresponding loss through collisions of electrons with heavy particles. The time dependent excitation is considered explicitly in form of a sinusoidal E/N, and the corresponding rate and transport coefficients are calculated with the aid of a two-term approximation Boltzmann-solver. Results for a discharge in helium with 0.5 percent molecular oxygen admixture are presented as well as a comparison with a more comprehensive one-dimensional fluid model for a 1 mm electrode gap.   

Manipulating electron dynamics and plasma chemistry in dual radio-frequency driven atmospheric pressure plasmas

Radio-frequency driven cold atmospheric pressure plasmas have the potential for many new technological applications. Plasma ionisation dynamics and chemistry is complex and increased control is desired. Dual frequency operation has been shown to provide enhanced control over power coupling and ionisation mechanisms [1, 2]. Here a numerical model based on hydrodynamic equations with a semi-kinetic treatment of the electrons considering 184 reactions amongst 20 species is used to determine the effects of dual-frequency excitation on electron dynamics and plasma chemistry. It is found that variations of the frequencies, voltages and relative phase enable the manipulation of the temporal and spatial structures of plasma ionisation and subsequently the electron energy distribution function (EEDF) which governs plasma chemistry. \\[4pt] [1] J. Waskoenig and T. Gans, Appl. Phys. Lett. 96, 181501 (2010). \\[0pt] [2] C.O'Neill, J. Waskoenig and T. Gans, IEEE Trans. Plasma Sci. (Accepted April 28, 2011).   

Modeling of Interactions between Surface properties, DC Self Bias and Plasma Stability in PECVD Tools

PECVD tools employing capacitively coupled plasma (CCP) sources are widely used in the semiconductor industry to deposit low-k dielectric materials. Power coupling in a CCP reactor is dominated by the plasma-sheath-surface dynamics. The properties of the electrode and other plasma-bounding surfaces, as well as the amount and type of material deposited thereon, affect such dynamics by modifying locally the plasma density, the electron temperature, and the DC self bias. Because PECVD tools are depositing tools, changes to the plasma properties due to surface modification are intrinsic of the process and unavoidable. The purpose of this work is to study these interactions between surface properties, secondary electron emission, DC self bias, plasma density and electron temperature by means of a fluid-type plasma model. Furthermore, the correlation between modeling results and some experimental results as a function of process parameters and chamber conditioning are reported and discussed.   

SiH4-H2-Plasma Modeling of the deposition of $\mu $c-Si:H Solar Cells

The correlation between plasma properties and characteristics of thin film silicon solar cells is relatively unknown. As a result, university researchers use numerous plasma sources for deposition of microcrystalline silicon by Plasma Enhanced Chemical Vapor Deposition (PECVD). Within industry, Capacitive Coupled Plasma (CCP) has been established as the standard source. It is known that different plasma species induce different performance properties in solar cells. This work seeks to establish this relationship between plasma chemistry and solar cell characteristics. In a preliminary analysis, the chemical reactions of SiH4-H2 were modeled in order to investigate the $\mu $c-Si:H deposition characteristics of different plasma sources. Using a global model, the ideal plasma regime for high-quality solar cells was determined with respect to electron density and temperature. To complement this model, CCP discharge was specifically analyzed using a fluid model from the commercial tool CFD-ACE+. These results were validated against experimental data for growth rate and SiH4 depletion from literature. The chemical plasma composition responsible for $\mu $c-Si:H layers was investigated and correlations were developed between measured cell efficiencies and simulated plasma species.   

Modeling of an Atmospheric Pressure Helium Plasma Jet

Cold atmospheric plasma jets have attracted great interest due to their potential application in fields such as biomedical surface modification. It is now well established that cold plasma jets produced by nanosecond pulsed discharges are in fact a series of rapidly propagating streamer discharges that have been termed ``plasma bullets.'' The goal of this work is to elucidate the role that the diffusion zone, air-helium interactive chemistry and photoionization play in the physics of a single plasma bullet discharge. In this work, we perform several simulations with helium in a 3 mm diameter cavity and a mixed helium-air ambient excited by a 10 kV positive pulse. We utilize a self-consistent, multi-species, two-temperature plasma model with helium-air chemistry and a three-term Helmholtz photoionization model. It was found that the presence of air, which has a higher ionization threshold than helium is crucial to the formation of the bullet. The self-induced electric fields produced at the streamer head at the air-helium interface are what drive the propagation and give the bullet its distinctive ring shape. Although not crucial to bullet formation, including air photoionization resulted in streamer speeds almost twice those seen when photoionization is not included.   

Symmetric multi-component diffusion modeling for Magnum PSI

Magnum PSI is a linear plasma generator for studying plasma surface interaction in conditions as expected in the ITER divertor. In Magnum PSI, the diffusive fluxes do not follow the simple Fick law for diffusion, due to coupling of the fluxes between species and directions, and ambipolar and magnetic fields. Instead they are described by the Stefan-Maxwell equations. In our contribution, we will address the numerical issues associated with solving the Stefan-Maxwell equations and the resulting set of continuity equations for the species. In particular, we will present a symmetric approach where all species are treated as independent unknowns and no species are singled out in order to account for mass and charge conservation. Modeling results of Magnum PSI using this approach will be presented.