LDRD final report : on the development of hybrid level-set/particle methods for modeling surface evolution during feature-scale etching and deposition processes.

Abstract

Two methods for creating a hybrid level-set (LS) / particle method for modeling surface evolution during feature-scale etching and deposition processes are developed and tested. The first method supplements the LS method by introducing Lagrangian marker points in regions of high curvature. Once both the particle set and the LS function are advanced in time, minimization of certain objective functions adjusts the LS function so that its zero contour is in closer alignment with the particle locations. It was found that the objective-minimization problem was unexpectedly difficult to solve, and even when a solution could be found, the acquisition of it proved more costly than simply expanding the basis set of the LS function. The second method explored is a novel explicit marker-particle method that we have named the grid point 3 particle (GPP) approach. Although not a LS method, the GPP approach has strong procedural similarities to certain aspects of the LS approach. A key aspect of the method is a surface rediscretization procedure-applied at each time step and based on a global background mesh-that maintains a representation of the surface while naturally adding and subtracting surface discretization points as the surface evolves in time. This method was coded in 2-D, and tested on a variety of surface evolution problems by using it in the ChISELS computer code. Results shown for 2-D problems illustrate the effectiveness of the method and highlight some notable advantages in accuracy over the LS method. Generalizing the method to 3D is discussed but not implemented.4