Numerical simulation of quantum effects in high-k gate dielectric MOS structures using quantum mechanical models

In this paper the electrical characteristics of metal oxide semiconductor (MOS) capacitors with high-k gate dielectric are investigated with quantum mechanical models. Both the self-consistent Schrödinger-Poisson (SP) model and the density gradient (DG) model are solved simultaneously to study quantum confinement effects (QCEs) for MOS capacitors. A computationally efficient parallel eigenvalue solution algorithm and a robust monotone iterative (MI) finite volume (FV) scheme for the SP and DG models are systematically proposed and successfully implemented on a Linux cluster, respectively. With the developed simulator, we can extract the effective gate oxide thickness from capacitance voltage (C-V) measurements for TaN and Al gate NMOS capacitors with Z_rO₂ and S_iO₂ gate dielectric materials. We found that quantization effects of 5.0 nm Z_rO₂ MOS samples cannot be directly equivalent to commonly quoted effects of 1.5 nm S_iO₂ MOS samples. Achieved benchmarks are also included to demonstrate excellent performances of the proposed computational techniques.