Plasma and BIAS Modeling: Self-Consistent Electrostatic-Particle-In-Cell with low Density Argon Plasma for TiC

Juergen Geiser , Sven Blankenburg

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 18 pp.

MSC 2000

60J20 Applications of discrete Markov processes

65C05 Monte Carlo methods

Abstract
We motivate our study by simulating the particle transport of a thin film deposition process done by PVD (physical vapor deposition) processes. In this paper we present a new model taken into account a self-consistent electrostatic-particle in cell model with low density Argon plasma. We propose a collision models for projectile and target collisions in order to compute the mean free path and include the virial coefficients that considered interacting and overlapping gas particles. The collision model are based of Monte Carlo simulations is discussed for DC sputtering in lower pressure regimes. We derive an equation for the mean free path for arbitrary interactions (cross sections) which (most important) includes the relative velocity between the projectiles and targets based on physical first principles and extend with higher order Virial terms. In order to simulate transport phenomena within sputtering processes realistically, a spatial and temporal knowledge of the plasma density and electrostatic field configuration is needed. Due to relatively low plasma densities, continuum fluid equations are not applicable. We propose instead a particle-tracking method. Particle-in-cell (PIC) methods allow the study of plasma behavior by computing the trajectories of finite-size particles under the action of an external and self-consistent electric field defined in a grid of points. Additionally, we apply the electric and magnetic field in the Lorentz forces to obtain a self-consistent electrostatic particle in cell model. At the target we simulate the deposition rates of the particles Ti and C based on the Monte Carlo simulations.