Parallel finite element method to solve the 3D Poisson equation and its application to abrupt heterojunction bipolar transistors

In this work we present a parallel solver for the Poisson equation for 3D abrupt heterojunction bipolar transistors (HBT). Three-dimensional simulation is essential for studying devices of small geometry as in the case we have studied. We have used an unstructured tetrahedral mesh and we have applied the finite method element (FEM), making a specific formulation for the nodes located on the interface of the regions with different characteristics. For HBT devices, it is necessary to take into account that on both sides of the interface between the different regions exist materials with different properties. Our formulation implies situating pairs of nodes in the same physical positions of the interface, associating each nodes to a region of the HBT. This way, the effects due to thermionic emission and the tunnel effect may be simulated when the Poisson and the electron and hole equations are solved in an abrupt HBT. We have applied domain decomposition methods to solve the associate linear systems. This code has been implemented for distributed memory multicomputers, making use of a message passing standard library, MPI.