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

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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.