Analysis of the hydrodynamic semiconductor device model - boundary conditions and simulations

A mathematical analysis of the time-dependent multi-dimensional Hydrodynamic model is performed to determine the well-posed boundary conditions for semiconductor device simulation. The number of independent boundary conditions that need to be specified at electrical contacts of a semiconductor device are derived. Using the classical energy method, a mathematical relation among the physical parameters is established to define the well-posed boundary conditions for the problem. Several possible sets of boundary conditions are given to illustrate the proper boundary conditions. Natural boundary conditions that can be specified are obtained from the boundary integrals of the weak-form finite element formulations. An example is included to illustrate the importance of well-posedness of the boundary conditions for device simulation.