Novel Modeling Approach to Analyze Threshold Voltage Variability in Short Gate-Length (15–22 nm) Nanowire FETs with Various Channel Diameters

Abstract

In this study, threshold voltage (Vth) variability was investigated in silicon nanowire field-effect transistors (SNWFETs) with short gate-lengths of 15–22 nm and various channel diameters (DNW) of 7, 9, and 12 nm. Linear slope and nonzero y-intercept were observed in a Pelgrom plot of the standard deviation of Vth (σVth), which originated from random and process variations. Interestingly, the slope and y-intercept differed for each DNW, and σVth was the smallest at a median DNW of 9 nm. To analyze the observed DNW tendency of σVth, a novel modeling approach based on the error propagation law was proposed. The contribution of gate-metal work function, channel dopant concentration (Nch), and DNW variations (WFV, ∆Nch, and ∆DNW) to σVth were evaluated by directly fitting the developed model to measured σVth. As a result, WFV induced by metal gate granularity increased as channel area increases, and the slope of WFV in Pelgrom plot is similar to that of σVth. As DNW decreased, SNWFETs became robust to ∆Nch but vulnerable to ∆DNW. Consequently, the contribution of ∆DNW, WFV, and ∆Nch is dominant at DNW of 7 nm, 9 nm, and 12, respectively. The proposed model enables the quantifying of the contribution of various variation sources of Vth variation, and it is applicable to all SNWFETs with various LG and DNW.