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

• Published in: Computer physics communications 2002-08, Vol.147 (1), p.214-217
• Main Authors: Li, Yiming, Lee, Jam-Wem, Tang, Ting-Wei, Chao, Tien-Sheng, Lei, Tan-Fu, Sze, S.M.
• Format: Article
• Language: English
• Subjects: Applied sciences; Electronics; Exact sciences and technology; High-k dielectric; Miscellaneous; MOS capacitor; Numerical methods; Quantum mechanical models; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Semiconductor-device characterization, design, and modeling
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/S0010-4655(02)00248-5

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 r O 2 and S i O 2 gate dielectric materials. We found that quantization effects of 5.0 nm Z r O 2 MOS samples cannot be directly equivalent to commonly quoted effects of 1.5 nm S i O 2 MOS samples. Achieved benchmarks are also included to demonstrate excellent performances of the proposed computational techniques.