With the ever-growing semi-conductor market the need for more advanced and faster chips rises. To keep the steady trend of Moore’s law going, which states that the transistors on a microchip double every two years, the micro chip manufacturing processes have to become more and more precise. The current state of the art Extreme Ultra Violet Light (EUV) lithography systems produced by ASML can manufacture chips with precision of printing up to 2 nanometers. At these scales even the smallest particles can affect the production processes of chips.
To circumvent the interference of molecules or debris in lithography machines flow simulations are performed to determine how to design flows to clear out these contaminants. Since most areas of the EUV machine are under rarefied gas conditions, normal continuum approaches fall short to predict the flow conditions. For rarefied flows the Direct Simulations Monte Carlo (DSMC) solver called SPARTA (Stochastic Parallel Rarefied-gas Time-accurate Analyzer) can be used. There are more methods to model rarefied gas flows, however the SPARTA program is open-source, adaptable and scales well on parallel computing systems. The last one of the three implies that simulations can be accelerated on High Performance Computing (HPC) clusters. Although the parallel computing accelerates the process, the simulations remain expensive. For instance, the 3D simulation of a scanner section contains 1 billion particles and needs a simulation power of 2000 cores for upwards of 45-80 hours of simulation time.
Consequently, it is necessary to continually develop methods to reduce computational costs for gas flow simulations. In particular cases where the contaminant concentration is so low that the effect of contaminants on the carrier gas can be neglected. In such cases the effects of a flow field on the contaminants can be passively modelled, and this method was dubbed the name Passive Scalar Approach (PSA). In other words, there are no carrier gas particles to actively participate in the collisions. The objective of this thesis is to reduce computational costs of a rarefied gas simulation with DSMC method on SPARTA by means of the PSA method.
First, the PSA capabilities were added to the SPARTA code. The PSA was implemented such that the steady-state background flow for a specific flow domain is first generated. Once this background flow field is imported into SPARTA, the contaminants can be loaded on top of the background flow with various concentrations, distributions, and at various locations within the simulation domain. The interactions between the contaminant and the background flow within every simulation cell is determined by the stream velocity of the background file, temperature and the velocity of the contaminant particles, using a Variable Soft Sphere (VSS) collision model. No active carrier gas particles need to be loaded into the memory of the solver.
Next, the PSA method was compared against a DSMC simulation with active carrier gas particles (referred to as a “full DSMC simulation”) for two cases: 1. Brownian motion in a box with homogenous carrier concentration, and 2. contaminant injection in a Poiseuille flow. Both cases showed similar diffusion rates indicating that the PSA models the full DSMC. In the Poiseuille flow case, an additional molecular scattering analysis showed similar scattering behaviour to the full DSMC collision model on a microscopic level. A significant decrease in computational costs was noted for the PSA in both cases. The findings in this thesis describe the promising results of implementing the PSA to model rarefied aerodynamic behaviour in SPARTA, with significant computational gains.