Another technique to describe moving boundaries over time is the LS method [86]. The surface is described as the zero LS of a continuous function defined on the entire simulation domain
The LS method is able to describe the position of the surface with sub-grid accuracy. Furthermore, this method allows an accurate calculation of geometric variables, such as the surface normal or the curvature. Similarly to cell-based methods, the implicit description of the surface position allows handling of topographic changes without special consideration.
After successful demonstrations for the applicability of the LS method to topography simulation [4,5,6,108], this technique has become the most popular technique to track a surface over time, especially in three dimensions. The LS method is used by many academic groups for two-dimensional [8,112,113] or three-dimensional topography simulation [46,65,96,98]. The topography simulators earlier developed at the Institute for Microelectronics at the Vienna University of Technology, as ELSA [40] and Topo3D [111], also use the LS method for surface evolution. Furthermore, the newer commercial topography simulators such as the two- and three-dimensional Victory process simulator by Silvaco [43,126], the two-dimensional Sentaurus Topography simulator by Synopsys [127], or PLENTE by Process-Evolution [16,17] are also based on the LS method.