Compact Models of the Quantized Sub-Band Energy Levels for MOSFET Device Application

The quantum confinement effect of the MOS structure at the silicon/oxide interface can be determined by solving the coupled Schrodinger and Poisson equations using a self-consistent numerical method. Computationally efficient compact models are usually determined from a triangular potential well approximation near the silicon/silicon-oxide interface. The triangular potential model is improved in [Yutao Ma, et. al. (2000)] at strong inversion by using the effective surface field. An analytical model based on the Wentzel-Kramer-Brillouin (WKB) asymptotic approximation of the coupled Schrodinger and Poisson equations is proposed in [H. Abebe, et. al. (2006)]. In this paper we compare results from the compact models of [Yutao Ma, et. al. (2000)] and [H. Abebe, et. al. (2006)] with SCHRED The results in figures 2 and 3 show that the two models give improvement over the original triangular potential well approximation [M. Stern (1972)] at strong inversion, but both show some differences in predicting the substrate doping effects on the quantum subband energy levels compared to SCHRED.