  In this article we propose and numerically implement a mathematical model for
the simulation of three-dimensional semiconductor devices characterized by an
heterogeneous material structure. The model consists of a system of nonlinearly
coupled time-dependent diffusion-reaction partial differential equations with
convection terms describing the principal electrical, thermal and chemical
phenomena that determine the macroscopic electrical response of the device
under the action of externally applied electrical and thermal forces. The
system is supplied with suitable initial, boundary and interface conditions
that account for the interaction occurring among the various regions of the
device with the surrounding environment. Temporal semi-discretization of the
problem is carried out with the Backward Euler Method while a fixed-point
iteration of Gummel type is used for system decoupling. Numerical approximation
of the linearized subproblems is carried out using an exponentially fitted
stabilized Finite Element Method on unstructured tetrahedral grids. Several
computational experiments are included to validate the physical accuracy of the
proposed computational algorithm in the study of realistic device structures.
