General 2D Schrödinger-Poisson solver with open boundary conditions for nano-scale CMOS transistors

• Published in: Journal of computational electronics Vol. 7; no. 4; pp. 475 - 484
• Main Authors: Pourghaderi, M. Ali, Magnus, Wim, Sorée, Bart, De Meyer, Kristin, Meuris, Marc, Heyns, Marc
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.12.2008; Springer; Springer Nature B.V
• Subjects: Algorithms; Applied sciences; Boundary conditions; Carrier density; CMOS; Conduction bands; Design. Technologies. Operation analysis. Testing; Eigenvectors; Electrical Engineering; Electronics; Ellipsoids; Engineering; Exact sciences and technology; Germanium; Integrated circuits; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mechanical Engineering; Metal oxide semiconductors; Molecular electronics, nanoelectronics; Optical and Electronic Materials; Quantum transport; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Silicon devices; Solvers; Theoretical; Transistors; Transmission; Two-dimensional Schrödinger-Poisson solver; Ballistic transport; Quantum transmitting boundary; Open boundary conditions; Ballistic transport; Boundary condition; Implementation; Nanoelectronics; Two-dimensional Schrödinger-Poisson solver; Coding; Complementary MOS technology; Silicon; MOS transistor; Effective mass; Open boundary conditions; Quantum transmitting boundary; Charge carrier density; Poisson equation; Two dimensional model; Density distribution; Algorithm; Schrödinger equation; High voltage; Germanium; Chemical potential; Drain voltage; NMOS technology; Conduction band; Quantum transport
• ISSN: 1569-8025; 1572-8137
• DOI: 10.1007/s10825-008-0257-8

Employing the quantum transmitting boundary (QTB) method, we have developed a two-dimensional Schrödinger-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 complicating the implementation of open boundary conditions. We present a generalized quantum transmitting boundary method that mainly leans on the completeness of the eigenstates 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.