Advanced plasma modeling tools that can simulate plasmas used for semiconductor processing

Fabrication of nanoelectronics devices requires processing of features with sub-10 nm dimensions, with some structures in logic and memory devices being less than 40 atoms wide. To achieve these goals, a multidisciplinary approach is needed that integrates and advances our understanding and predictability of complex processes involving plasma chemistry, plasma-surface interactions, and surface science. Correspondingly, modelling capabilities include particle-in-cell (PIC) codes to model low-pressure discharges and quantum chemistry codes to calculate volume and surface chemistries, and ML/AI techniques to develop reaction pathways.

For plasma processing, there is a need to simulate large plasma devices via kinetic means, because the Electron Velocity Distribution Function in these devices is non-Maxwellian and therefore a fluid treatment is insufficient to accurately capture the physics. The method of choice for many fully kinetic simulations has been the particle-in-cell (PIC) technique due to relatively ease of implementation of the method and that it can be parallelized effectively over many processors and accelerated on GPUs. However, PIC codes that use standard explicit schemes are constrained by the requirement to resolve the short length and time scales associated with the plasma Debye radius and plasma frequency respectively [1]. This makes it extremely challenging to perform long time 2D PIC simulations for large plasma devices. For this reason, many 2D kinetic simulations of plasmas have been limited to small or artificially scaled systems. Energy conserving [2] or implicit methods [3] must be used to remove these limitations. Effects of numerical noise in simulations using PIC code need to be analyzed and taken into account [1]. The PIC codes have been applied to study plasma processing applications, such as capacitively coupled plasmas, electron beam produced plasmas, inductively coupled, hollow cathodes [4-9]. To model surface processes we used a combination of quantum chemistry methods and molecular dynamics [10-13]. For analysis of chemical reaction pathways, we employed direct sensitivity analysis and an uncertainty-aware strategy for plasma mechanism reduction with directed weighted graphs [14].