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提出了一种基于物理的MOS电容超薄氧化层量子隧穿解析模型,量子力学效应在应用奇异微扰法求解密度梯度方程时得以体现。将泊松方程和经量子修正的电子势方程同时求解,得出电子和静电势在垂直于沟道方向的分布。结果反映出量子效应明显不同于经典物理学的预测。对解析解结果和精确的数值模拟进行比较,结果表明,在栅极偏压和氧化层厚度的较大变化范围内,二者都能很好地吻合。
A physics-based quantum tunneling analysis model of ultrathin MOS oxide layer is proposed. Quantum mechanics effects are demonstrated when using the singular perturbation method to solve the density gradient equation. The Poisson equation and the quantum-modified electron potential equation are solved simultaneously, and the distribution of the electron and electrostatic potential perpendicular to the channel direction is obtained. The results show that the quantum effect is significantly different from the prediction of classical physics. The results of the analytical solution and the exact numerical simulation are compared. The results show that both of them are in good agreement with the larger variation of gate bias and oxide thickness.