Work-Function Fluctuation of Gate-All-Around Silicon Nanowire n-MOSFETs: A Unified Comparison Between Cuboid and Voronoi Methods

In this article, the work-function fluctuation (WKF) of nanosized metal grains is estimated and compared with the cuboid and Voronoi methods for 10-nm-gate gate-all-around silicon nanowire n-MOSFETs. For the methods having different metal grain numbers (MGNs) and 1000 randomly generated samples, we evaluate the variability of the threshold voltage, off-current and on-current. The estimated errors of figures-of-merit (FOM) above are within 1% between the cuboid and Voronoi methods when the sample increases (e.g., larger than 500) for all MGNs. If a small number of samples are with few metal grains (e.g., MGN = 16), they affect the normal distribution of FOM and cause large error due to the significant random location effect of metal grains. If the Voronoi method generates grains are with acute angles, abrupt changes of electric fields occur among grain boundaries. For large samples, errors of FOM are all within 1% because distributions of FOM follow the Gauss distribution. Thus, the results of this work suggest that the WKF-induced variability calculated by the cuboid method can well approximate to the results of Voronoi method for sufficient large samples.