The solution approach
The coating process was realized on the EOSS® sputtering facility at the Fraunhofer IST. This system consists of two sputter compartments with cylindrical double-tube cathodes which are sputtered in argon, above which a fast-rotating turn table is mounted to which the substrates are attached. In an additional RF plasma source, the complete oxidation of the sub-layers takes place in an oxygen plasma. For rotationally symmetric 3D substrates, a special sample holder with built-in sub-rotation is utilized, whereby the layer-thickness profile is adjusted through special shaper masks at the compartment edges.
The multi-scale simulation model is used to specify the design of the shaper masks. The plasma, as well as the gas flow and transport of the sputtered particles, can be simulated using a kinetic software developed at the Fraunhofer IST in which the “Direct Simulation Monte-Carlo” (DSMC) and “Particle-in-Cell Monte-Carlo” (PIC-MC) methods are combined. Two practical problems thereby are the computational effort - approx. 1 day for DSMC and several days for PIC-MC - and the fact that the layer-thickness profile on moving substrates results from the addition of many sub-profiles from different positions. With the previous methods, this procedure is therefore considerably too time-consuming.
With a multi-scale approach, these problems are solved as follows: Firstly, the plasma and the sputter erosion profile at the target are determined using the PIC-MC method (see Figs. 1, 2). This information is subsequently used to simulate the transport and scattering of sputtered particles (see Fig. 3). The angle-resolved particle flow is thereby recorded in a plane a few millimeters below the substrates with a spatial resolution of 10x10 mm². Using this plane as a “virtual particle source”, the remaining particle transport up to the substrate is subsequently calculated using a simple ray-tracing approach, during which the shaper mask can simultaneously be taken into account in parameterized form. This approach is possible as the remaining distance lies below the mean free path and the scattering with the gas can therefore be neglected. The ray-tracing algorithm enables the calculation of a complete motion trajectory within a few seconds on a single CPU and can therefore be regarded as a “digital twin” for the coating process on 3D substrates.