Large-scale simulations of intrinsic parameter fluctuations in nano-scale MOSFETs

Intrinsic parameter fluctuations have become a serious obstacle to the continued scaling of MOSFET devices, particularly in the sub-100 nm regime. The increase in intrinsic parameter fluctuations means that simulations on a statistical scale are necessary to capture device parameter distributions. In this work, large-scale simulations of samples of 100,000s of devices are carried out in order to accurately characterise statistical variability of the threshold voltage in a real 35 nm MOSFET. Simulations were performed for the two dominant sources of statistical variability – random discrete dopants (RDD) and line edge roughness (LER). In total ∼400,000 devices have been simulated, taking approximately 500,000 CPU hours (60 CPU years). The results reveal the true shape of the distribution of threshold voltage, which is shown to be positively skewed for random dopants and negatively skewed for line edge roughness. Through further statistical analysis and data mining, techniques for reconstructing the distributions of the threshold voltage are developed. By using these techniques, methods are demonstrated that allow statistical enhancement of random dopant and line edge roughness simulations, thereby reducing the computational expense necessary to accurately characterise their effects. The accuracy of these techniques is analysed and they are further verified against scaled and alternative device architectures. The combined effects of RDD and LER are also investigated and it is demonstrated that the statistical combination of the individual RDD and LER-induced distributions of threshold voltage closely matches that obtained from simulations. By applying the statistical enhancement techniques developed for RDD and LER, it is shown that the computational cost of characterising their effects can be reduced by 1–2 orders of magnitude