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Simulation in thin film technology
Progressive cost and quality requirements in thin film technology increasingly demand more efficient and precise coating processes. However, the size and complexity of these processes makes development with purely empirical means difficult. Process simulation becomes indispensable here in order to obtain the required insights into process dynamics and relevant parameter correlations. Presuming valid models, simulation can partly substitute for experimental evaluation in process and system development. This saves time and costs that would be expended on experimental setups and measurements.
Viable simulation approaches
Chemical vapour deposition in a high vacuum has established itself for industrial high-precision thin film coatings on large surfaces. Prominent methods are thermal vaporisation, magnetron sputtering and plasma-activated chemical vapour deposition. The process conditions for these methods are characterised by high Knudsen numbers for the process gases (low-pressure range) and low ionisation levels for the plasmas (low-temperature plasma). Common computational fluid dynamics (CFD) simulations based on continuum mechanics or the Navier-Stokes equation are not applicable in this parameter area. For example, the continuum assumption of a homogeneous electron speed is generally invalid in gyrokinetic plasmas and plasma edge layers. Statistical non-equilibrium thermodynamics as described by the Boltzmann transport equation apply here instead. But unlike CFD simulation, only few simulation programs are available based on the Boltzmann transport equation.
The DSMC/PIC-MC method
Suitable methods to solve the Boltzmann transport equation in the parameter area mentioned above are the Direct Simulation Monte Carlo (DSMC) and the Particle-in-Cell Monte Carlo (PIC-MC) method. In both cases the distribution density function of the Boltzmann transport equation is modelled using representative macro-particles in a numeric computational grid. Particle dynamics in the spatial and speed domain are calculated within discrete time steps and under consideration of the field, wall and particle interactions. Here the PIC-MC method complements the DSMC method with field solvers and algorithms used to calculate the interactions between charged particles and the electromagnetic field. The particle states for the respective time steps and grid cells form the statistical, place and time-resolved solution of the Boltzmann transport equation for the gas or plasma. To filter the noise component from this statistical solution, the particle states are averaged over several time steps and particles per cell.