Two-dimensional quantum mechanical simulation of charge distribution in silicon MOSFETs

A solver for the two-dimensional (2-D) Schrodinger equation based on the k-space representation of the solution has been developed and applied to the simulation of 2-D electrostatic quantum effects in nano-scale MOS transistors. This paper presents the mathematical framework of the simulator, addresses the related accuracy and efficiency problems, and discusses the simulations performed to validate it. Furthermore, the 2-D quantum effects observed in the simulation of charge densities in tens-hundreds nanometer scale MOS structures are described.