General 2d Schroedinger-poisson Solver With Open Boundary Conditions For Nano-scale Cmos Transistors

摘要

Employing the quantum transmitting boundary (QTB) method, we have developed a two-dimensional Schrodinger-Poisson solver in order to investigate quantum transport in nano-scale CMOS transistors subjected to open boundary conditions. In this paper we briefly describe the building blocks of the solver that was originally written to model silicon devices. Next, we explain how to extend the code to semiconducting materials such as germanium, having conduction bands with energy ellipsoids that are neither parallel nor perpendicular to the channel interfaces or even to each other. The latter introduces mixed derivatives in the 2D effective mass equation, thereby heavily com- plicating the implementation of open boundary conditions. We present a generalized quantum transmitting boundary method that mainly leans on the completeness of the eigen-states of the effective mass equation. Finally, we propose a new algorithm to calculate the chemical potentials of the source and drain reservoirs, taking into account their mutual interaction at high drain voltages. As an illustration, we present the potential and carrier density profiles obtained for a (111) Ge NMOS transistor as well as the ballistic current characteristics.