Variability of Threshold Voltage Induced by Work-Function Fluctuation and Random Dopant Fluctuation on Gate-All-Around Nanowire nMOSFETs

We advance the localized work-function fluctuation (LWKF) method to examine the variability of threshold voltage $(\mathrm{V}_{\mathrm{t}\mathrm{h}})$ induced by titanium nitride (TiN) metal-gate work-function fluctuation (WKF) and combined the WKF with the random dopant fluctuation (RDF) for various grain sizes on Si gate-all-around (GAA) nanowire (NW) MOSFETs. Our results show that the WKF-induced variability of $\mathrm{V}_{\mathrm{t}\mathrm{h}}$ will be dominated by bamboo-type TiN grains and its impact is larger than that induced by the RDF with doped channel (RDF (doped)). Additionally, the variability of $\mathrm{V}_{\mathrm{t}\mathrm{h}}$ induced by the WKF and the RDF (doped) could be treated as independent fluctuation sources because the channel dopants are away from the metal-gate/high-$\kappa$ interface. Consequently, statistical models are further proposed for the $\sigma\mathrm{V}_{\mathrm{t}\mathrm{h}}$ induced by the WKF and the combined WKF with RDF (doped) by considering position effect of nanosized TiN grains.