Unified Quantum and Reliability Model for Ultra-Thin Double-Gate MOSFETs

This paper presents a unified two-dimensional (2D) threshold voltage model for lightly doped symmetrical double-gate p-channel MOSFETs including quantum confinement effects and negative bias temperature instability (NBTI). The proposed model has been derived by solving the two-dimensional Poisson equation to obtain the NBTI potential model and the one-dimensional Schrödinger equation together with the 2D Poisson equation to obtain the quantum confinement model. The quantum expression was subsequently embedded in the NBTI solution to reach a unified model for both quantum confinement and NBTI. The model is simple and continuous, thereby ensuring compatibility for insertion in Verilog-A based device simulators. The effect of stress time on the degradation of the threshold voltage has been measured over a 10 year period. The accuracy of the model has been validated through comparisons with both 2D numerical simulations and experimental data. The results show matching within ±3% for channel lengths down to 7 nm and silicon thicknesses of 5 nm at 1 GHz operation after 10 years.