Monte Carlo simulations concerning elastic scattering with application to DC and high power pulsed magnetron sputtering for Ti_3SiC_2

Juergen Geiser , Sven Blankenburg

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 27 pp.

MSC 2000

65C05 Monte Carlo methods

60J20 Applications of discrete Markov processes

Abstract
We motivate our studying on simulating thin film deposition processes that can be done by sputtering processes. In the last years, the research in producing high temperature films by depositing of low pressure processes have increased. Due to standard applications in deposing TiN and TiC, that are immense, recently also deposition with new material classes known as MAX-phases became be more and more important. The MAX-phase are nanolayered terniar metal-carbides or -nitrids, where M is a transition metal, A is an A-group element (e.g. Al, Ga, In, Si, etc.) and X is C (carbon) or N (nitrid). We present a particle tracking model for low temperature and low pressure plasma. Several collision models are presented for projectile and target collisions in order to compute the mean free path and the differential cross section (angular distribution of scattered projectiles) of the scattering process. The detailed description of collision models is of highest importance in Monte Carlo Simulations of high power pulsed magnetron sputtering and DC sputtering. We derive an equation for the mean free path for arbitrary interactions (cross sections) that include the relative velocity between the particles. We apply our results to two major interaction models: hard sphere interaction and Screened Coulomb interaction. Both types of interaction separates DC sputtering from HPPMS. Further investigations presented in this paper involve modifications of the scattering angle probability distribution due to initially moving background targets. In order to tackle this modification, an appropriate Monte-Carlo-Markov-Chain approach is proposed.