Efficient simulation of the full Coulomb interaction in three dimensions

The continued scaling of MOSFETs into the nano-scale regime requires refined models for carrier transport due to, e.g., unintentional doping in the active channel region which gives rise to threshold voltage and on-state current fluctuations. Therefore every transport simulator which is supposed to accurately simulate nano-devices must have a proper model for the inclusion of the Coulomb interactions. This paper proposes to use a 3D FMM (fast multi-pole method) (Greengard and Rokhlin, 1997; Cheng et al., 1999). The FMM is based on the idea of condensing the information of the potential generated by point sources in series expansions. After calculating expansions in a hierarchical manner, the long-range part of the potential is obtained by evaluating the series at the point in question and the short-range part is calculated by direct summation. Its computational effort is only O(n) where n is the number of particles. In summary, the use of the FMM approach for semiconductor transport simulations was validated. Simulation times are decreased significantly and effects due to electron-electron and electron-impurity interactions are observed as expected. Since the FMM algorithm operates independently of the grid used in the MC simulation, it can be easily included into existing MC device simulation codes.