The three-dimensional device simulation has become a necessary tool for the design and investigation of complex device structures. The evolution of the three-dimensional simulation tools is directly linked to the scaling of the devices and the increasing complex ity of dynamic random access memory (DRAM) cells. Scaling of MOSFET devices led to a three-dimensional geometry with effects which cannot be handled by two-dimensional simulations anymore. With increasing integration density in DRAMs the third dimen sion had to be utilized to realize the storage capacitor. The result ing leakage problems have to be investigated and the cell design optimized by means of three-dimensional simulations. This book is intended for senior undergraduate students in applied physics, electrical engineering and computational physics, as well as for scientists and engineers involved in semiconductor device re search and development. It is also intended for software engineers and all those who are concerned with simulation. The book will give an overview on the problems and activities con cerning three-dimensional device simulation, without the claim of being a classical textbook. It starts from the classical semiconduc tor equations, discusses the physical models used in device simu lation, describes the discretization and some numerical methods for solving the differential equations. The application of the three dimensional simulation to VLSI device engineering is illustrated by a few specific examples."