Wavelet-based adaptive mesh generation for device simulation

A new method to define the discretization grid to solve semiconductor devices PDE systems is reported. A multiresolution approach is implemented to achieve adaptively refined grids that can be fruitfully used to get a solution with the same level of accuracy of a reference case, but with a considerable lower number of points. The proposed algorithm defines an automatic procedure that requires neither the user-feedback control nor an in-depth physical knowledge of the problem to be solved, and it is accurate enough to describe all important physical effects encountered in a number of practical situations. To this aim, it provides the possibility to dynamically adjust the mesh in order to capture the solution variations during a sweep simulation. Some 2D practical examples will be discussed (a power p–n junction and a planar MOSFET) to demonstrate (i) how the wavelet-refined grids preserve geometrical and physical consistency, and (ii) the efficiency and reliability of the proposed approach in terms of computational cost and solution accuracy. It is worth to notice that, due to its simplicity, the presented method can be efficiently extended to perform multidimensional analysis and it can be carried out within a typical TCAD environment.