Effective density-of-states approach to QM correction in MOS structures

MOS structure threshold voltage shift due to quantum mechanical effects (QMEs) has a substantial influence on deep-submicron MOSFET characteristics. However, its physical nature has not been thoroughly investigated and an analytical model is absent. In this paper, a numerical solution of the Schrodinger equation with parabolic potential well and an analytical solution with triangular well are compared, and the validity of the triangular well approximation is verified. Based on the calculation of the subband structure in the quantized region in a weak inversion regime, the concepts of surface layer effective density-of-states (SLEDOS) is proposed. Carrier distribution in subbands is then analyzed and physical base of MOSFETs Vth shift due to QMEs are discussed. The single subband occupation approximation used in earlier works is proved to be invalid and a new analytical threshold voltage (Vth) shift model due to QMEs including multisubband occupation is derived based on the concept of SLEDOS. The model reveals the physical nature of QMEs on Vth shift and gives consistent results with experiments and self-consistent calculation.