Device Modeling of Discrete Impurities for the Analyses of Threshold Voltage Fluctuations in Ultrasmall Semiconductor Devices

我们建立了研究超小型si- mosfet阈值电压波动的准一维解析模型。此外，还研究了我们所建立的离散杂质模型在三维漂移扩散模拟方案中的物理意义和有效性。结果总结如下：1。建立了阈值电压波动的准一维解析模型，并首次导出了mosfet中阈值电压的精确概率分布函数。研究发现，当器件尺寸缩小到10 nm以下时，典型块体mosfet的概率密度开始大大偏离预期的高斯分布。通过改变mosfet衬底中的杂质分布，研究了两种不同的广泛使用的杂质模型（原子模型和果冻模型）在漂移扩散模拟中的物理意义和有效性。与原子模型和果冻杂质模型中获得的电位分布的巨大差异相比，已经发现器件特性没有显着变化。我们已经证明，器件特性与负责集体载流子运动的长期宏观势有关。因此，我们的杂质模型中提取的库仑势的长程部分与我们刚刚发现的图像是一致的。

We have constructed the quasi-1D analytical model for the investigation of threshold voltage fluctuations in ultra-small Si-MOSFETs. Also, the physical meaning and the validity of discrete impurity model we have developed for 3D Drift-Diffusion simulation scheme have been studied. The results are summarized as follows.1.The quasi-1D analytical model for threshold voltage fluctuations has been constructed and the exact probability distribution function for threshold voltage in MOSFETs has been derived for the first time.2.It has been found that the probability density for typical bulk MOSFETs begins to greatly deviate from the expected Gaussian distribution as the device size shrinks below sub-10 nm.3.The physical meaning and the validity of the two different widely-used impurity models (atomistic and jelly) for Drift-Diffusion simulations are studied by changing the impurity profiles in the substrate of MOSFETs. It has been found that the device characteristics do not change significantly, in contrast with the large differences in the potential profiles obtained from the atomistic and jelly impurity models.4.We have shown that the device characteristics are associated with the long-ranged macroscopic potential which is responsible to collective carrier motion. As a result, our impurity model in which the long-range part of the Coulomb potential is extracted is consistent with the picture we have just found.