The presented simulations and models function fully within the process simulator presented in [50]. The LS method is utilized in order to describe the top surface of a semiconductor wafer as well as the interfaces between different materials. The LS method describes a movable surface as the zero LS of a continuous function defined on the entire simulation domain,
(1) 
(2) 
The LS equation can be solved using numerical schemes developed for the solution of HamiltonJacobi equations, since the LS equation belongs to the class of HamiltonJacobi equations, given by
(4) 
(5) 
(6) 
The initially proposed LS method uses a LS function which is defined on the entire simulation domain. However, memory requirements for the discretization of the LS function scale with domain size. Therefore, alternatives were proposed in the form of the narrow band method, where only a few layers around the LS surface are active grid points, and sparse field method [226], where a single layer of active grid points are considered for time integration. The steps required to implement the utilized process simulator are described by [50]
(7) 
For the calculation of finite difference schemes, the LS framework needs only to store the LS values of defined grid points, which is the union of all active grid points and their neighbors. The HRLE data structure [83] is used in order to store the discretized LS function. This structure is a hybrid between the DTG and the RLE data structures. It combines the linear scaling memory requirements of the DTG with adaptation to all grid directions. The HRLE data structure is organized hierarchically, similar to the DTG, where in place of storing a sequence of defined grid points, RLE is applied. Therefore, the structure is capable of storing the sign of the LS function for undefined grid points, while having the memory consumption of a DTG structure. The details of the implementation and examples showing the differences between the different data structures are described in [50]
Another important aspect of the LS framework is the ability to describe multiple LS surfaces for different material regions. The definition of different material regions in the LS framework was designed with etching processes in mind. When simulating traditional semiconductor processes, deposition is usually performed on the top layer, making masking not necessary. However, etching is almost always a masked process. Therefore the mask must be identifiable within the multiLS framework. Figure 1.2 shows how material regions are labeled, resulting in an etchfriendly environment. When material needs to be etched, with serving as a mask, the LS defined by needs to be moved in the negative direction, but only at the locations where it is not touching the surface.

If material is deposited or grown with serving as a mask, it is evident that the LS definitions from Figure 1.2b will result in the material deposition on top of , which is undesired. Therefore, when needs to be grown with serving as a mask, as is the case with the oxidation process, the LS definition and numbering must be changed.