Application of the self-consistent quantum method for simulating the size quantization effect in the channel of a nano-scale dual gate MOSFET

Self-Consistent Quantum Method using Schrodinger-Poisson equations have been used for determining the Channel electron density of Nano-Scale MOSFETs for 6nm and 9nm thick channels. The 6nm thick MOSFET show the peak of the electron density at the middle where as the 9nm thick MOSFET shows the accumulation of the electrons at the oxide/semiconductor interface. The electron density in the channel is obtained from the diagonal elements of the density matrix; [ρ]=[1/(1+exp(β(H − μ)))] A Tridiagonal Hamiltonian Matrix [H] is constructed for the oxide/channel/oxide 1D structure for the dual gate MOSFET. This structure is discretized and Finite-Difference method is used for constructing the matrix equation. The comparison of these results which are obtained by Quantum methods are done with Semi-Classical methods