Application of the Density Matrix Formalism for Obtaining the Channel Density of a Dual Gate Nanoscale Ultra-Thin MOSFET and its Comparison with the Semi-Classical Approach

Abstract

Density Matrix Formalism using quantum methods has been used for determining the channel density of dual gate ultra-thin MOSFETs. The results obtained from the quantum methods have been compared with the semi-classical methods. This paper discusses in detail the simulation methods using self-consistent schemes and the discretization procedures for constructing the Hamiltonian Matrix for a dual gate MOSFET consisting of oxide/semiconductor/oxide interface and the self-consistent procedure involving the discretization of Poisson’s equation for satisfying the charge neutrality condition in the channel of different thicknesses. Under quantum methods, the channel densities are determined from the diagonal elements of the density matrix. This successfully simulates the size quantization effect for thin channels. For semi-classical methods, the Fermi–Dirac Integral function is used for the determination of the channel density. For thin channels, the channel density strongly varies with the values of the effective masses. This variation is simulated when we use Quantum methods. The channel density also varies with the asymmetric gate bias and this variation is more for thicker channels where the electrons get accumulated near the oxide/semiconductor interface. All the calculations are performed at room temperature (300K).