Phenomenological modeling of low-bias sulfur hexafluoride plasma etching of silicon

Low-bias etching of silicon (Si) using sulfur hexafluoride (SF6) plasma is a valuable tool in the manufacturing of electronic devices and microelectromechanical systems (MEMS). This kind of etching offers an almost isotropic etching behaviour, since the low voltage bias does not provide enough vertical acceleration and kinetic energy to the ions. Due to this near-isotropic behavior, the aforementioned plasma etching finds application as an alternative to wet etching in, e.g., MEMS and optical applications since it provides a cleaner and more precisely controllable process. However, the degree of isotropy and, consequently, the final surface profile remain difficult to control. In this work, we apply a three-dimensional feature-scale topography simulation to low-bias SF6 etching experiments in Si to aid in process development and to investigate the physical etching mechanisms which govern the final surface geometry. We achieve this by accurately reproducing three distinct experimental data sets and by discussing the meaning of the phenomenological model parameters involved in the topography simulation in detail. We show that our phenomenological top-down flux calculation approach more accurately reproduces the experimental results than conventional strictly isotropic and bottom-up approaches. The reactor loading effect is taken into account as a general reduction of the model etch rates, which is supported by comparing simulated to experimentally determined etch depths in different loading regimes. Our model is also able to accurately reproduce reported trench geometries for different mask openings and etch times using a single parameter set for a given reactor configuration. Hence, we propose that the model parameters, in particular the average effective sticking coefficient, can be taken as a proxy of the reactor configuration. We provide an empirical relationship linking the average sticking coefficient of a reactor recipe to a measurable degree of isotropy of etched geometries. This empirical relationship can be used in practice to (i) estimate the average effective sticking coefficient of independent experiments and to (ii) fine-tune the etched geometry.